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

<b>let </b><font color="Maroon" title="c1">k</font> be  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">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="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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#V7" title="AMI_1:attr.7">definite</a> <a href="ami_1.html#V14" title="AMI_1:attr.14">standard-ins</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="c2">N</font>;<br/><b>let </b><font color="Maroon" title="c4">I</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font>;<br/>







<b>set </b><font color="Maroon" title="c5">A</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">J</font></span>)</span> where <font color="Olive" title="b1">J</font> is   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">J</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c6">B</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">J</font></span>)</span> where <font color="Olive" title="b1">J</font> is   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font> :  <a href="ami_1.html#K19" title="AMI_1:func.19">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="c4">I</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">J</font> </span>}</span> ;<br/>
<a NAME="E1:74"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">J</font></span>)</span> where <font color="Olive" title="b1">J</font> is   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">J</font> </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">J</font></span>)</span> where <font color="Olive" title="b1">J</font> is   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font> :  <a href="ami_1.html#K19" title="AMI_1:func.19">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="c4">I</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">J</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>proof </b></a><div class="add">

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon" title="c7">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:74_1_1"/>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">J</font></span>)</span> where <font color="Olive" title="b1">J</font> is   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">J</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c8">J</font> being   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font><b> such that </b><br/><a NAME="E3:74_1_1"/><i><font color="Green" title="E39">A1</font></i>: 
<font color="Maroon" title="c7">a</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="c8">J</font>
 <b>and </b><br/><a NAME="E4:74_1_1"/><i><font color="Green" title="E40">A2</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c8">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c4">I</font>
 ;<br/><a NAME="E5:74_1_1"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c8">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">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="c4">I</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:74_1_1"><i><font color="Green" title="E40">A2</font></i></a>, <a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>;<br/><b>hence </b><a NAME="E6:74_1_1"/>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">J</font></span>)</span> where <font color="Olive" title="b1">J</font> is   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font> :  <a href="ami_1.html#K19" title="AMI_1:func.19">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="c4">I</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">J</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:74_1_1"><i><font color="Green" title="E39">A1</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c7">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:74_1"/>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">J</font></span>)</span> where <font color="Olive" title="b1">J</font> is   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font> :  <a href="ami_1.html#K19" title="AMI_1:func.19">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="c4">I</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">J</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c8">J</font> being   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font><b> such that </b><br/><a NAME="E4:74_1"/><i><font color="Green" title="E39">A3</font></i>: 
<font color="Maroon" title="c7">a</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="c8">J</font>
 <b>and </b><br/><a NAME="E5:74_1"/><i><font color="Green" title="E40">A4</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c8">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">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="c4">I</font>,<font color="Maroon" title="c1">k</font></span>)</span>
 ;<br/>
<a NAME="E6:74_1"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c8">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c4">I</font>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E5:74_1"><i><font color="Green" title="E40">A4</font></i></a>, <a class="ref" href="amistd_2.html#D14" target="_self" title="AMISTD_2:def.14">Def14</a></i>;<br/>
<b>hence </b><a NAME="E7:74_1"/>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressPart</a> <font color="Olive" title="b1">J</font></span>)</span> where <font color="Olive" title="b1">J</font> is   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <font color="Maroon" title="c3">S</font> :  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c4">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Olive" title="b1">J</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:74_1"><i><font color="Green" title="E39">A3</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:74"/>
 <a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_2.html#K5" title="AMISTD_2:func.5">AddressParts</a> <span class="p1">(<span class="default"><a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</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">I</font>,<font color="Maroon" title="c1">k</font></span>)</span></span>)</span>
 ;<br/>


</div>
