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

<b>thus </b><a NAME="E1:107_1_1"/>
 <a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font> is <a href="amistd_2.html#V2">homogeneous</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_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>, <font color="Maroon">J</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#D4">AMISTD_2:def 4</a><br/>

<b>assume </b><a NAME="E1:107_1_1_1"/><i><font color="Green">E50</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">J</font>
 ;<br/>

<a NAME="E2:107_1_1_1"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">J</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">J</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">J</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">J</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">J</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">J</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">J</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">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K8">:=</a> <font color="Olive">r</font> )
 
<b>by </b><i><a class="ref" href="scmring2.html#T8">SCMRING2:8</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_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="E1:107_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="107_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_1"/><i><font color="Green">E64</font></i>: 
<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="E2:107_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/><a NAME="E3:107_1_1_1_1_1"/><b>then </b>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:107_1_1_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T13" target="_self">Th13</a>, <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="107_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:107_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="E3:107_1_1_1_1_2"/><i><font color="Green">E67</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="E4:107_1_1_1_1_2"/><i><font color="Green">E68</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_1_1_1_1_2_1_1"/>
( <font color="Maroon">J</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">J</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">J</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">J</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">J</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">J</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">J</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">J</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="107_1_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_2_1_1_1"/>
<font color="Maroon">J</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="E2:107_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">J</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="E3:107_1_1_1_1_2_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_2_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">J</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">d1</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">d2</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:107_1_1_1_1_2_1_1_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_2_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">J</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">J</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">J</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">J</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">J</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">J</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>hence </b><a NAME="E2:107_1_1_1_1_2_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , , , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:107_1_1_1_1_2"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:107_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="E3:107_1_1_1_1_3"/><i><font color="Green">E104</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="E4:107_1_1_1_1_3"/><i><font color="Green">E112</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_1_1_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_1_1_1_1_3_1_1"/>
( <font color="Maroon">J</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">J</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">J</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">J</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">J</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">J</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">J</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">J</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="107_1_1_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_3_1_1_1"/>
<font color="Maroon">J</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="E2:107_1_1_1_1_3_1_1_1"/><b>then </b>
<font color="Maroon">J</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="E3:107_1_1_1_1_3_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_3_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">J</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">d1</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">d2</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:107_1_1_1_1_3_1_1_2"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_3_1_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_3_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">J</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">J</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">J</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">J</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">J</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">J</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>hence </b><a NAME="E2:107_1_1_1_1_3_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , , , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:107_1_1_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_4"><b>suppose </b></a><a NAME="E1:107_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="E3:107_1_1_1_1_4"/><i><font color="Green">E156</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="E4:107_1_1_1_1_4"/><i><font color="Green">E157</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_1_1_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_1_1_1_1_4_1_1"/>
( <font color="Maroon">J</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">J</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">J</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">J</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">J</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">J</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">J</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">J</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="107_1_1_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_4_1_1_1"/>
<font color="Maroon">J</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="E2:107_1_1_1_1_4_1_1_1"/><b>then </b>
<font color="Maroon">J</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="E3:107_1_1_1_1_4_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_4_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">J</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">d1</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">d2</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:107_1_1_1_1_4_1_1_2"/><i><font color="Green">E158</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_4_1_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_4_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">J</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">J</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">J</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">J</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">J</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">J</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>hence </b><a NAME="E2:107_1_1_1_1_4_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , , , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:107_1_1_1_1_4"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_5"><b>suppose </b></a><a NAME="E1:107_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="E3:107_1_1_1_1_5"/><i><font color="Green">E159</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="E4:107_1_1_1_1_5"/><i><font color="Green">E160</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 4
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_1_1_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_1_1_1_1_5_1_1"/>
( <font color="Maroon">J</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">J</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">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">J</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">J</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">J</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">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">J</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">J</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">J</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="107_1_1_1_1_5_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_5_1_1_1"/>
<font color="Maroon">J</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="E2:107_1_1_1_1_5_1_1_1"/><b>then </b>
<font color="Maroon">J</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="E3:107_1_1_1_1_5_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_5_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_5_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">J</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">d1</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">d2</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:107_1_1_1_1_5_1_1_2"/><i><font color="Green">E161</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Maroon">d1</font>,<font color="Maroon">d2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_5_1_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_5_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">J</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">J</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">J</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">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">J</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">J</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">J</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>hence </b><a NAME="E2:107_1_1_1_1_5_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , , , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:107_1_1_1_1_5"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_6"><b>suppose </b></a><a NAME="E1:107_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="E3:107_1_1_1_1_6"/><i><font color="Green">E162</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="E4:107_1_1_1_1_6"/><i><font color="Green">E164</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 6
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_1_1_6_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_1_1_1_1_6_1_1"/>
( <font color="Maroon">J</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">i2</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">J</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Olive">i2</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">J</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">J</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">J</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">J</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">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">J</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">J</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="107_1_1_1_1_6_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_6_1_1_1"/>
<font color="Maroon">J</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="E2:107_1_1_1_1_6_1_1_1"/><b>then </b>
<font color="Maroon">J</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="E3:107_1_1_1_1_6_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_6_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_6_1_1_2"/>
 ex <font color="Olive">i2</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">J</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Olive">i2</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">i2</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="E3:107_1_1_1_1_6_1_1_2"/><i><font color="Green">E165</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Maroon">i2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 1
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i2</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_6_1_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_6_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">J</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">J</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">J</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">J</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">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">J</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">J</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>hence </b><a NAME="E2:107_1_1_1_1_6_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , , , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:107_1_1_1_1_6"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_7"><b>suppose </b></a><a NAME="E1:107_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="E3:107_1_1_1_1_7"/><i><font color="Green">E166</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="E4:107_1_1_1_1_7"/><i><font color="Green">E167</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 7
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_1_1_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_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="E1:107_1_1_1_1_7_1_1"/>
( <font color="Maroon">J</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">d1</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">i2</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">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">d1</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Olive">i2</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">J</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">J</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">J</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">J</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">J</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">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <font color="Maroon">J</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="107_1_1_1_1_7_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_7_1_1_1"/>
<font color="Maroon">J</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="E2:107_1_1_1_1_7_1_1_1"/><b>then </b>
<font color="Maroon">J</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="E3:107_1_1_1_1_7_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_7_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_7_1_1_2"/>
 ex <font color="Olive">d1</font> being   <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font> ex <font color="Olive">i2</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">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">d1</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Olive">i2</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">d1</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">i2</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="E3:107_1_1_1_1_7_1_1_2"/><i><font color="Green">E168</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d1</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i2</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i2</font>,<font color="Maroon">d1</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_7_1_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_7_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">J</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">J</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">J</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">J</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">J</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">r</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <font color="Maroon">J</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>hence </b><a NAME="E2:107_1_1_1_1_7_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , , , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:107_1_1_1_1_7"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_8"><b>suppose </b></a><a NAME="E1:107_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="E3:107_1_1_1_1_8"/><i><font color="Green">E169</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="E4:107_1_1_1_1_8"/><i><font color="Green">E170</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 5
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_1_1_8_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_1_1_1_1_8_1_1"/>
( <font color="Maroon">J</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> 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">J</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmring2.html#K8">:=</a> <font color="Olive">r</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">J</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">J</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">J</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">J</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">J</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">J</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> )
 </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="107_1_1_1_1_8_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_8_1_1_1"/>
<font color="Maroon">J</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="E2:107_1_1_1_1_8_1_1_1"/><b>then </b>
<font color="Maroon">J</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="E3:107_1_1_1_1_8_1_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_8_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_8_1_1_2"/>
 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">J</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">b</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">r1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:107_1_1_1_1_8_1_1_2"/><i><font color="Green">E171</font></i>: 
<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">r1</font>
 ;<br/><b>thus </b> <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">r</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> 2
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">r1</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_8_1_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_8_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">J</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">J</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">J</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">J</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">J</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">J</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>hence </b><a NAME="E2:107_1_1_1_1_8_1_1_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , , , , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:107_1_1_1_1_8"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">J</font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<b>thus </b><a NAME="E2:107_1_1"/>
 <a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font> is <a href="amistd_2.html#V5">with_explicit_jumps</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_2"><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#D8">AMISTD_2:def 8</a><br/><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D6">AMISTD_2:def 6</a><br/>



<b>assume </b><a NAME="E1:107_1_1_2"/><i><font color="Green">E190</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_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> 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="107_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_2_1_1"/><i><font color="Green">E191</font></i>: 
<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="E2:107_1_1_2_1_1"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5">halt</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E3:107_1_1_2_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T13" target="_self">Th13</a>, <a class="ref" href="scmring2.html#T30">SCMRING2:30</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_2_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="E3:107_1_1_2_1_2"/><i><font color="Green">E192</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="E4:107_1_1_2_1_2"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:107_1_1_2_1_2"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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#T12" target="_self">Th12</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="107_1_1_2_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_2_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="E3:107_1_1_2_1_3"/><i><font color="Green">E193</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="E4:107_1_1_2_1_3"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmring2.html#K5">AddTo</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:107_1_1_2_1_3"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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#T12" target="_self">Th12</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="107_1_1_2_1_4"><b>suppose </b></a><a NAME="E1:107_1_1_2_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="E3:107_1_1_2_1_4"/><i><font color="Green">E194</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="E4:107_1_1_2_1_4"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:107_1_1_2_1_4"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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#T12" target="_self">Th12</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="107_1_1_2_1_5"><b>suppose </b></a><a NAME="E1:107_1_1_2_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="E3:107_1_1_2_1_5"/><i><font color="Green">E195</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="E4:107_1_1_2_1_5"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmring2.html#K7">MultBy</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:107_1_1_2_1_5"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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#T12" target="_self">Th12</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="107_1_1_2_1_6"><b>suppose </b></a><a NAME="E1:107_1_1_2_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="E3:107_1_1_2_1_6"/><i><font color="Green">E196</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="E4:107_1_1_2_1_6"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E5:107_1_1_2_1_6"/><b>then </b><i><font color="Green">E197</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T13" target="_self">Th13</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>take </b>
1
;<br/><a NAME="E6:107_1_1_2_1_6"/><i><font color="Green">E198</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><a href="scmring2.html#K9">goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i/>;<br/><a NAME="E7:107_1_1_2_1_6"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/><b>hence </b><a NAME="E8:107_1_1_2_1_6"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T13" target="_self">Th13</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>thus </b><a NAME="E9:107_1_1_2_1_6"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</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#T13" target="_self">Th13</a>, <a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_2_1_7"><b>suppose </b></a><a NAME="E1:107_1_1_2_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="E3:107_1_1_2_1_7"/><i><font color="Green">E199</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="E4:107_1_1_2_1_7"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E5:107_1_1_2_1_7"/><b>then </b><i><font color="Green">E200</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T13" target="_self">Th13</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>take </b>
1
;<br/><a NAME="E6:107_1_1_2_1_7"/><i><font color="Green">E201</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i/>;<br/><a NAME="E7:107_1_1_2_1_7"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 2
 <b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/><b>hence </b><a NAME="E8:107_1_1_2_1_7"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring3.html#T13" target="_self">Th13</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>thus </b><a NAME="E9:107_1_1_2_1_7"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</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#T13" target="_self">Th13</a>, <a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, , <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_2_1_8"><b>suppose </b></a><a NAME="E1:107_1_1_2_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="E3:107_1_1_2_1_8"/><i><font color="Green">E202</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="E4:107_1_1_2_1_8"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">r</font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>hence </b><a NAME="E5:107_1_1_2_1_8"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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#T12" target="_self">Th12</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>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#D9">AMISTD_2:def 9</a><br/><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D7">AMISTD_2:def 7</a><br/>



<b>given </b><font color="Maroon">k</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E3:107_1_1"/><i><font color="Green">E203</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>and </b><br/><a NAME="E4:107_1_1"/><i><font color="Green">E204</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E5:107_1_1"/><i><font color="Green">E205</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</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="E6:107_1_1"/><i><font color="Green">E206</font></i>: 
 <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</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/>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_1_1_3"/>
( <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="107_1_1_3_1"><b>suppose </b></a><a NAME="E1:107_1_1_3_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="E2:107_1_1_3_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/><a NAME="E3:107_1_1_3_1"/><b>then </b>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:107_1_1_3_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><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="107_1_1_3_2"><b>suppose </b></a><a NAME="E1:107_1_1_3_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="E3:107_1_1_3_2"/><i><font color="Green">E207</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="E4:107_1_1_3_2"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><a NAME="E5:107_1_1_3_2"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:107_1_1_3_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_3_3"><b>suppose </b></a><a NAME="E1:107_1_1_3_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="E3:107_1_1_3_3"/><i><font color="Green">E208</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="E4:107_1_1_3_3"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><a NAME="E5:107_1_1_3_3"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:107_1_1_3_3"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_3_4"><b>suppose </b></a><a NAME="E1:107_1_1_3_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="E3:107_1_1_3_4"/><i><font color="Green">E209</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="E4:107_1_1_3_4"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><a NAME="E5:107_1_1_3_4"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:107_1_1_3_4"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_3_5"><b>suppose </b></a><a NAME="E1:107_1_1_3_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="E3:107_1_1_3_5"/><i><font color="Green">E210</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="E4:107_1_1_3_5"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><a NAME="E5:107_1_1_3_5"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:107_1_1_3_5"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmring3.html#T1" target="_self">Th1</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_3_6"><b>suppose </b></a><a NAME="E1:107_1_1_3_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="E3:107_1_1_3_6"/><i><font color="Green">E211</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="E4:107_1_1_3_6"/><i><font color="Green">E212</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><a NAME="E5:107_1_1_3_6"/><b>then </b>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, </i>;<br/><a NAME="E6:107_1_1_3_6"/><b>then </b><i><font color="Green">E213</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T13" target="_self">Th13</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, <a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>;<br/><a NAME="E7:107_1_1_3_6"/>
 <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><b>hence </b><a NAME="E8:107_1_1_3_6"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_3_7"><b>suppose </b></a><a NAME="E1:107_1_1_3_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="E3:107_1_1_3_7"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">i1</font>
 ;<br/><a NAME="E4:107_1_1_3_7"/><i><font color="Green">E215</font></i>: 
 <a href="amistd_2.html#K4">AddressPart</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">i1</font>,<font color="Maroon">a</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><a NAME="E5:107_1_1_3_7"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, </i>;<br/><a NAME="E6:107_1_1_3_7"/><b>then </b><i><font color="Green">E216</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T13" target="_self">Th13</a>, <a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, , <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/><a NAME="E7:107_1_1_3_7"/>
 <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">i1</font></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><b>hence </b><a NAME="E8:107_1_1_3_7"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T18" target="_self">Th18</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_3_8"><b>suppose </b></a><a NAME="E1:107_1_1_3_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="E3:107_1_1_3_8"/><i><font color="Green">E217</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="E4:107_1_1_3_8"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">r</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scmring3.html#T12" target="_self">Th12</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><a NAME="E5:107_1_1_3_8"/><b>then </b><i><font color="Green">E218</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i/>;<br/><a NAME="E6:107_1_1_3_8"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, </i>;<br/><a NAME="E7:107_1_1_3_8"/><b>then </b>
<span class="p1">(<span class="default"><a href="amistd_2.html#K1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_2.html#K3">SCM-Instr-Loc</a> 
 <b>by </b><i><a class="ref" href="scmring1.html#D2">SCMRING1:def 2</a></i>;<br/><b>hence </b><a NAME="E8:107_1_1_3_8"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T14" target="_self">Th14</a>, <a class="ref" href="scmring3.html#T15" target="_self">Th15</a>, <a class="ref" href="scmring3.html#T16" target="_self">Th16</a>, <a class="ref" href="scmring3.html#T17" target="_self">Th17</a>, , <a class="ref" href="scmring2.html#D1">SCMRING2:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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