<?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">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/>







<b>assume </b><a NAME="E1:74"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</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">x</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>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D12" target="_self">AMISTD_2:def 12</a><br/>

<b>set </b><font color="Maroon">f</font> =  <a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font>;<br/>
<a NAME="E2:74"/><i><font color="Green">E45</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> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:74"/><i><font color="Green">E56</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>,<font color="Maroon">k</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">I</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:74"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</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#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="Olive">x</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">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:74_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">x</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>
 ;<br/>

<a NAME="E2:74_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">x</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">x</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/>
<b>hence </b><a NAME="E3:74_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> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</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">x</font>
 <b>by </b><i><a class="ref" href="amistd_2.html#T3" target="_self">Th3</a>, <a class="ref" href="amistd_2.html#T4" target="_self">Th4</a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:74"/><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> <font color="Maroon">I</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K4" target="_self">AddressPart</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E2:74"><i><font color="Green">E45</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<b>hence </b><a NAME="E6:74"/>
 <a href="amistd_2.html#K8" target="_self">IncAddr</a> <font color="Maroon">I</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:74"><i><font color="Green">E44</font></i></a>, </i>;<br/>


</div>
