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

<b>let </b><font color="Maroon">a</font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">S</font>, <font color="Maroon">b</font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:72_1_2"/><i><font color="Green">E83</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E2:72_1_2"/><i><font color="Green">E132</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>and </b><br/><a NAME="E3:72_1_2"/><i><font color="Green">E133</font></i>: 
for <font color="Olive">n</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> holds <br/>( ( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> implies  ex <font color="Olive">f</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> st <br/>( <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Olive">f</font></span>)</span></span>)</span> ) ) &amp; ( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> implies <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> ) )
 <b>and </b><br/><a NAME="E4:72_1_2"/><i><font color="Green">E134</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E5:72_1_2"/><i><font color="Green">E135</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span>
 <b>and </b><br/><a NAME="E6:72_1_2"/><i><font color="Green">E136</font></i>: 
for <font color="Olive">n</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> holds <br/>( ( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> implies  ex <font color="Olive">f</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> st <br/>( <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Olive">f</font></span>)</span></span>)</span> ) ) &amp; ( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> implies <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> ) )
 ;<br/>

<a NAME="E7:72_1_2"/><i><font color="Green">E137</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E8:72_1_2"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:72_1_2_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:72_1_2_1"/><b>then </b>
( ( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> implies  ex <font color="Olive">f</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> st <br/>( <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Olive">f</font></span>)</span></span>)</span> ) ) &amp; ( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> implies <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> ) &amp; ( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> implies  ex <font color="Olive">f</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font> st <br/>( <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> &amp; <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Olive">f</font></span>)</span></span>)</span> ) ) &amp; ( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" target="_self">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" target="_self">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> implies <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> ) )
 
<b>by </b><i><a class="ref" href="amistd_2.html#T2" target="_self">Th2</a>, , , <a class="ref" href="amistd_2.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E3:72_1_2_1"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E9:72_1_2"/><b>then </b>
 <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="amistd_2.html#T2" target="_self">Th2</a>, , <a class="ref" href="amistd_2.html#T4" target="_self">Th4</a>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>
<b>hence </b><a NAME="E10:72_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T3" target="_self">Th3</a>, </i>;<br/>


</div>
