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

<b>let </b><font color="Maroon" title="c1">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a> <a href="amistd_1.html#V4" title="AMISTD_1:attr.4">standard</a> <a href="amistd_2.html#V8" title="AMISTD_2:attr.8">regular</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">I</font>, <font color="Maroon" title="c4">J</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c2">S</font>;<br/>





<b>given </b><font color="Maroon" title="c5">k</font> being  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><a NAME="E1:79"/><i><font color="Green" title="E47">A1</font></i>: 
 <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">k</font>
 ;<br/>

<i><font color="Green" title="E48">A2</font></i>:  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">I</font> = 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">k</font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>
<br/>.= 
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c4">J</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:79"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>
;<br/>
<a NAME="E3:79"/><b>then </b><i><font color="Green" title="E49">A3</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c4">J</font></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_2.html#D4" target="_self" title="AMISTD_2:def.4">Def4</a></i>;<br/>
<a NAME="E4:79"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c3">I</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_2"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:79_2"/><i><font color="Green" title="E50">A4</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c3">I</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:79_2_1"/>
( <span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> or <span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_2_1_1"><b>suppose </b></a><a NAME="E1:79_2_1_1"/><i><font color="Green" title="E51">A5</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c7">f</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E3:79_2_1_1"/><i><font color="Green" title="E52">A6</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <b>and </b><br/><a NAME="E4:79_2_1_1"/><i><font color="Green" title="E53">A7</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c7">f</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:79_2"><i><font color="Green" title="E50">A4</font></i></a>, <a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>;<br/><a NAME="E5:79_2_1_1"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:79"><i><font color="Green" title="E47">A1</font></i></a>, <a class="txt" href="amistd_2.html#E1:79_2_1_1"><i><font color="Green" title="E51">A5</font></i></a>, <a class="ref" href="amistd_2.html#T32" target="_self" title="AMISTD_2:th.32">Th32</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">g</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E7:79_2_1_1"/><i><font color="Green" title="E54">A8</font></i>: 
<font color="Maroon" title="c8">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <b>and </b><br/><a NAME="E8:79_2_1_1"/><i><font color="Green" title="E55">A9</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c8">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:79"><i><font color="Green" title="E49">A3</font></i></a>, <a class="txt" href="amistd_2.html#E1:79_2"><i><font color="Green" title="E50">A4</font></i></a>, <a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>;<br/><a NAME="E9:79_2_1_1"/>
<font color="Maroon" title="c5">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c7">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c8">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:79"><i><font color="Green" title="E47">A1</font></i></a>, <a class="txt" href="amistd_2.html#E4:79_2_1_1"><i><font color="Green" title="E53">A7</font></i></a>, <a class="txt" href="amistd_2.html#E8:79_2_1_1"><i><font color="Green" title="E55">A9</font></i></a>, <a class="ref" href="amistd_1.html#T25" title="AMISTD_1:th.25">AMISTD_1:25</a></i>;<br/><a NAME="E10:79_2_1_1"/><b>then </b>
 <a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c8">g</font>
 ;<br/><b>hence </b><a NAME="E11:79_2_1_1"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:79_2_1_1"><i><font color="Green" title="E52">A6</font></i></a>, <a class="txt" href="amistd_2.html#E7:79_2_1_1"><i><font color="Green" title="E54">A8</font></i></a>, <a class="ref" href="amistd_1.html#T27" title="AMISTD_1:th.27">AMISTD_1:27</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="79_2_1_2"><b>suppose </b></a><a NAME="E1:79_2_1_2"/><i><font color="Green" title="E51">A10</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">I</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font>
 ;<br/><div class="add"><a NAME="E2:79_2_1_2"/><b>then </b><i><font color="Green" title="E52">A11</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K1" title="AMISTD_2:func.1">PA</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c4">J</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:79"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="amistd_2.html#T33" target="_self" title="AMISTD_2:th.33">Th33</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <font color="Maroon" title="c3">I</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:79_2"><i><font color="Green" title="E50">A4</font></i></a>, <a class="txt" href="amistd_2.html#E1:79_2_1_2"><i><font color="Green" title="E51">A10</font></i></a>, <a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c4">J</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:79"><i><font color="Green" title="E47">A1</font></i></a>, <a class="txt" href="amistd_2.html#E3:79"><i><font color="Green" title="E49">A3</font></i></a>, <a class="txt" href="amistd_2.html#E1:79_2"><i><font color="Green" title="E50">A4</font></i></a>, <a class="txt" href="amistd_2.html#E2:79_2_1_2"><i><font color="Green" title="E52">A11</font></i></a>, <a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E5:79"/><b>then </b>
 <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Maroon" title="c4">J</font>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E3:79"><i><font color="Green" title="E49">A3</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>
<b>hence </b><a NAME="E6:79"/>
<font color="Maroon" title="c3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">J</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:79"><i><font color="Green" title="E48">A2</font></i></a>, <a class="ref" href="amistd_2.html#T16" target="_self" title="AMISTD_2:th.16">Th16</a></i>;<br/>


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