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

<b>let </b><font color="Maroon">j</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">k</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">R</font> be  <a href="scmring1.html#V1">good</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><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>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:44"/><i><font color="Green">E45</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span>
 ;<br/>

<b>then </b><i><font color="Green">E57</font></i>:  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p4">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">j</font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<font color="Maroon">j</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <span class="p1">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmring3.html#T67">SCMRING3:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p3">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmring2.html#K11">Next</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="scmring3.html#T67">SCMRING3:67</a></i>
;<br/>
<div><i><font color="Green">E61</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="44_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be   <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>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ami_1.html#D13">AMI_1:def 13</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ami_5.html#T81">AMI_5:81</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ami_1.html#D13">AMI_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ami_5.html#T81">AMI_5:81</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E4:44"/><i><font color="Green">E62</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="xxreal_0.html#R1">&lt;=</a> 7
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_3"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 7 )
 </span><b>by </b><i>, <a class="ref" href="cqc_the1.html#T8">CQC_THE1:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_1"><b>suppose </b></a><a NAME="E1:44_3_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:44_3_1"/><b>then </b><i><font color="Green">E70</font></i>: 
<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="scmring3.html#T16">SCMRING3:16</a></i>;<br/><a NAME="E3:44_3_1"/><i><font color="Green">E74</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</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>,<font color="Maroon">k</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="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><b>thus </b> <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="ami_1.html#D8">AMI_1:def 8</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_2"><b>suppose </b></a><a NAME="E1:44_3_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">db</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:44_3_2"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T17">SCMRING3:17</a></i>;<br/><a NAME="E4:44_3_2"/><i><font color="Green">E77</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K4">:=</a> <font color="Maroon">db</font>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:44_3_2"/><b>then </b><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>;<br/><i><font color="Green">E79</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T79">AMI_5:79</a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma38</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T79">AMI_5:79</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_3_2_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_2_2_1_1"><b>suppose </b></a><a NAME="E1:44_3_2_2_1_1"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_2_2_1_2"><b>suppose </b></a><a NAME="E1:44_3_2_2_1_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T13">SCMRING2:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:44_3_2"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_3"><b>suppose </b></a><a NAME="E1:44_3_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">db</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:44_3_3"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T18">SCMRING3:18</a></i>;<br/><a NAME="E4:44_3_3"/><i><font color="Green">E83</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K5">AddTo</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:44_3_3"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>;<br/><i><font color="Green">E85</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T79">AMI_5:79</a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma38</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T79">AMI_5:79</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_3_3_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_3_2_1_1"><b>suppose </b></a><a NAME="E1:44_3_3_2_1_1"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_3_2_1_2"><b>suppose </b></a><a NAME="E1:44_3_3_2_1_2"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T14">SCMRING2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:44_3_3"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_4"><b>suppose </b></a><a NAME="E1:44_3_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">db</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:44_3_4"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T19">SCMRING3:19</a></i>;<br/><a NAME="E4:44_3_4"/><i><font color="Green">E116</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K6">SubFrom</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:44_3_4"/><b>then </b><i><font color="Green">E117</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>;<br/><i><font color="Green">E118</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T79">AMI_5:79</a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma38</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T79">AMI_5:79</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_4_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_3_4_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_4_2_1_1"><b>suppose </b></a><a NAME="E1:44_3_4_2_1_1"/><i><font color="Green">E119</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_4_2_1_2"><b>suppose </b></a><a NAME="E1:44_3_4_2_1_2"/><i><font color="Green">E120</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T15">SCMRING2:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:44_3_4"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_5"><b>suppose </b></a><a NAME="E1:44_3_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">db</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:44_3_5"/><i><font color="Green">E121</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T20">SCMRING3:20</a></i>;<br/><a NAME="E4:44_3_5"/><i><font color="Green">E122</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K7">MultBy</a> <font color="Maroon">da</font>,<font color="Maroon">db</font>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:44_3_5"/><b>then </b><i><font color="Green">E123</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>;<br/><i><font color="Green">E124</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T79">AMI_5:79</a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma38</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T79">AMI_5:79</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_5_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_3_5_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_5_2_1_1"><b>suppose </b></a><a NAME="E1:44_3_5_2_1_1"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">db</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_5_2_1_2"><b>suppose </b></a><a NAME="E1:44_3_5_2_1_2"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T16">SCMRING2:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:44_3_5"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_6"><b>suppose </b></a><a NAME="E1:44_3_6"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</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="E3:44_3_6"/><i><font color="Green">E127</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">r</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T21">SCMRING3:21</a></i>;<br/><a NAME="E4:44_3_6"/><i><font color="Green">E129</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K8">:=</a> <font color="Maroon">r</font>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T29">AMISTD_2:29</a></i>;<br/><a NAME="E5:44_3_6"/><b>then </b><i><font color="Green">E130</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>;<br/><i><font color="Green">E131</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T79">AMI_5:79</a>, <a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma38</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T79">AMI_5:79</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_6_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_6_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_3_6_2_1"/>
( <font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_6_2_1_1"><b>suppose </b></a><a NAME="E1:44_3_6_2_1_1"/><i><font color="Green">E132</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<font color="Maroon">r</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_6_2_1_2"><b>suppose </b></a><a NAME="E1:44_3_6_2_1_2"/><i><font color="Green">E133</font></i>: 
<font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T19">SCMRING2:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:44_3_6"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_7"><b>suppose </b></a><a NAME="E1:44_3_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">loc</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="E3:44_3_7"/><i><font color="Green">E134</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T22">SCMRING3:22</a></i>;<br/><a NAME="E4:44_3_7"/><i><font color="Green">E135</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K9">goto</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E5:44_3_7"/><i><font color="Green">E136</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>;<br/><i><font color="Green">E137</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon">loc</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i><a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma38</font></i></a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T79">AMI_5:79</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_7_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T17">SCMRING2:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:44_3_7"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_8"><b>suppose </b></a><a NAME="E1:44_3_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">da</font> being    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>, <font color="Maroon">loc</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="E3:44_3_8"/><i><font color="Green">E138</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K10">=0_goto</a> <font color="Maroon">loc</font>
 <b>by </b><i><a class="ref" href="scmring3.html#T23">SCMRING3:23</a></i>;<br/><a NAME="E4:44_3_8"/><i><font color="Green">E139</font></i>: 
 <a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">da</font> <a href="scmring2.html#K10">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i>, </i>;<br/><div><i><font color="Green">E140</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_8_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_3_8_1_1"/>
( <font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> or <font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_8_1_1_1"><b>suppose </b></a><a NAME="E1:44_3_8_1_1_1"/><i><font color="Green">E141</font></i>: 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><a NAME="E2:44_3_8_1_1_1"/><b>then </b><i><font color="Green">E142</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 <b>by </b><i/>;<br/><a NAME="E3:44_3_8_1_1_1"/><i><font color="Green">E143</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">loc</font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
 <b>by </b><i>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<font color="Maroon">loc</font>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i><a class="txt" href="scmring4.html#E2"><i><font color="Green">Lemma41</font></i></a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T79">AMI_5:79</a></i>
;<br/><b>hence </b><a NAME="E5:44_3_8_1_1_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_8_1_1_2"><b>suppose </b></a><a NAME="E1:44_3_8_1_1_2"/><i><font color="Green">E144</font></i>: 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 ;<br/><div class="add"><a NAME="E2:44_3_8_1_1_2"/><b>then </b><i><font color="Green">E145</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">da</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font>
 <b>by </b><i/>;<br/><a NAME="E3:44_3_8_1_1_2"/><i><font color="Green">E146</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <span class="p2">(<span class="default"><a href="scmring2.html#K1">SCM</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>;<br/> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="scmring2.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="ami_5.html#T79">AMI_5:79</a>, <a class="txt" href="scmring4.html#E2"><i><font color="Green">Lemma41</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T79">AMI_5:79</a></i>
;<br/><b>hence </b><a NAME="E5:44_3_8_1_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_8_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be    <a href="scmring2.html#M1">Data-Location</a> of <font color="Maroon">R</font>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
<font color="Maroon">s</font> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i>, <a class="ref" href="scmring2.html#T18">SCMRING2:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p0">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="scmring2.html#K3">.</a> <font color="Maroon">d</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:44_3_8"/>
 <a href="ami_1.html#K4">Exec</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="amistd_2.html#K8">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmring4.html#K1" target="_self">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="txt" href="scmring4.html#E1"><i><font color="Green">Lemma38</font></i></a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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