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

<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">m</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">N</font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a> <a href="amistd_1.html#V4">standard</a> <a href="amistd_2.html#V8" target="_self">regular</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <font color="Maroon">S</font>;<br/>









<i><font color="Green">E44</font></i>:  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span> = 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font>
<b>by </b><i/>
<br/>.= 
 <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<i><font color="Green">E45</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> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> = 
 <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>by </b><i/>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E3:82"/>
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> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span></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> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:82_3"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">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> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:82_3"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">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> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:82_3"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">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>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:82_3_1"/>
( <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> or <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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_3_1_1"><b>suppose </b></a><a NAME="E1:82_3_1_1"/><i><font color="Green">E59</font></i>: 
<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>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">f</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:82_3_1_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E4:82_3_1_1"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span></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="Maroon">f</font></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E5:82_3_1_1"/>
<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> <span class="p4">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span></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>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T3" target="_self">Th3</a></i>;<br/><b>then consider </b><font color="Maroon">g</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E7:82_3_1_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E8:82_3_1_1"/><i><font color="Green">E65</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span></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">m</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">g</font></span>)</span></span>)</span>
 <b>by </b><i>, </i>;<br/><b>consider </b><font color="Maroon">h</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E10:82_3_1_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">h</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>and </b><br/><a NAME="E11:82_3_1_1"/><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</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>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">h</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E12:82_3_1_1"/>
 <a href="amistd_1.html#K7">locnum</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:82_3"><i><font color="Green">E56</font></i></a>, <a class="txt" href="amistd_2.html#E2:82_3"><i><font color="Green">E57</font></i></a>, <a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>;<br/><b>hence </b><a NAME="E13:82_3_1_1"/>
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span></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> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="txt" href="amistd_2.html#E3:82_3"><i><font color="Green">E58</font></i></a>, <a class="txt" href="amistd_2.html#E1:82_3_1_1"><i><font color="Green">E59</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="82_3_1_2"><b>suppose </b></a><a NAME="E1:82_3_1_2"/><i><font color="Green">E79</font></i>: 
<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>
 ;<br/><div class="add"><a NAME="E2:82_3_1_2"/><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> <span class="p4">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span></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>
 <b>by </b><i/>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
<b>by </b><i>, </i>
<br/>.= 
<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>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
<b>by </b><i>, , </i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E4:82"/><b>then </b>
 <a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4" target="_self">AddressPart</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<b>hence </b><a NAME="E5:82"/>
 <a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1" target="_self">Def1</a>, </i>;<br/>


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