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

<b>set </b><font color="Maroon">P</font> = <font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font>;<br/>
<b>set </b><font color="Maroon">k</font> = <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1;<br/>
<b>let </b><font color="Maroon">f</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D17">AMISTD_1:def 17</a><br/>

<b>assume </b><a NAME="E1:132_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
 ;<br/>

<a NAME="E2:132_1_1"/><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:132_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E13:132_1_1"><i><font color="Green">E65</font></i></a></i>;<br/>
<a NAME="E4:132_1_1"/><b>then </b><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E5:132_1_1"/><i><font color="Green">E57</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E6:132_1_1"/><i><font color="Green">E58</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Olive">m</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E7:132_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon">s2</font> being   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E9:132_1_1"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">s2</font></span>)</span>
 <b>and </b><br/><a NAME="E10:132_1_1"/><i><font color="Green">E62</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E11:132_1_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">s2</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>,<font color="Maroon">f</font>
 ;<br/>
<a NAME="E12:132_1_1"/><i><font color="Green">E64</font></i>: 
 <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>,<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="amistd_2.html#T10" target="_self">Th10</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>;<br/>
<a NAME="E13:132_1_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5">pi</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="132_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:132_1_1_1"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> or <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> )
 </span><b>by </b><i><a class="ref" href="amistd_2.html#T10" target="_self">Th10</a>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="132_1_1_1_1"><b>suppose </b></a><a NAME="E1:132_1_1_1_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:132_1_1_1_1"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="amistd_1.html#D17">AMISTD_1:def 17</a></i>;<br/><a NAME="E3:132_1_1_1_1"/>
not <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>then </b><font color="Maroon">s2</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:132_1_1_1_1"><i><font color="Green">E79</font></i></a>, , <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
 <a href="ami_5.html#K5">pi</a> <font color="Maroon">F</font>,<font color="Maroon">f</font>
<b>by </b><i>, , <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
;<br/><a NAME="E5:132_1_1_1_1"/><b>then </b>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">s2</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span>,<font color="Maroon">f</font>
 <b>by </b><i/>;<br/><a NAME="E6:132_1_1_1_1"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 <b>by </b><i>, </i>;<br/><a NAME="E7:132_1_1_1_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E8:132_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E14"><i><font color="Green">Lemma84</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="132_1_1_1_2"><b>suppose </b></a><a NAME="E1:132_1_1_1_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:132_1_1_1_2"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">f</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="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:132_1_1_1_2"/><i><font color="Green">E83</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E5:132_1_1_1_2"/><i><font color="Green">E132</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E14"><i><font color="Green">Lemma84</font></i></a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E6:132_1_1_1_2"/><b>then </b><i><font color="Green">E133</font></i>: 
 <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#D17">AMISTD_1:def 17</a></i>;<br/><a NAME="E7:132_1_1_1_2"/><i><font color="Green">E134</font></i>: 
 <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <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="ami_1.html#D11">AMI_1:def 11</a></i>;<br/><b>then reconsider </b><font color="Maroon">v</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> as    <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="ami_1.html#T59">AMI_1:59</a></i>;<br/><b>set </b><font color="Maroon">s1</font> = <font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font>;<br/><i><font color="Green">E135</font></i>:  <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>,<font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font>
<b>by </b><i>, <a class="txt" href="amistd_2.html#E3:132_1_1_1_2"><i><font color="Green">E82</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E4:132_1_1_1_2"><i><font color="Green">E83</font></i></a>, <a class="txt" href="amistd_2.html#E14"><i><font color="Green">Lemma84</font></i></a>, </i>
;<br/><a NAME="E10:132_1_1_1_2"/><i><font color="Green">E136</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/><a NAME="E11:132_1_1_1_2"/><i><font color="Green">E137</font></i>: 
 <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E12:132_1_1_1_2"/><i><font color="Green">E154</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E13:132_1_1_1_2"/><i><font color="Green">E155</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="amistd_2.html#T12" target="_self">Th12</a>, , , <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/><a NAME="E14:132_1_1_1_2"/><i><font color="Green">E183</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><b>reconsider </b><font color="Maroon">w</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> as    <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</font> <b>by </b><i>, <a class="ref" href="ami_1.html#T59">AMI_1:59</a></i>;<br/><a NAME="E16:132_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <font color="Maroon">w</font> is   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font>
 ;<br/><a NAME="E17:132_1_1_1_2"/><b>then </b><i><font color="Green">E184</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E18:132_1_1_1_2"/>
for <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s2</font> holds <br/><font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="132_1_1_1_2_2"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:132_1_1_1_2_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s2</font>
 ;<br/>

<a NAME="E2:132_1_1_1_2_2"/><i><font color="Green">E185</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="132_1_1_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:132_1_1_1_2_2_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="132_1_1_1_2_2_1_1"><b>suppose </b></a><a NAME="E1:132_1_1_1_2_2_1_1"/><i><font color="Green">E186</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> = 
 <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"><a href="amistd_1.html#K7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="amistd_2.html#E4:132_1_1_1_2"><i><font color="Green">E83</font></i></a>, , <a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, , <a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="132_1_1_1_2_2_1_2"><b>suppose </b></a><a NAME="E1:132_1_1_1_2_2_1_2"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font>
 ;<br/><div class="add"><a NAME="E2:132_1_1_1_2_2_1_2"/><b>then </b><i><font color="Green">E188</font></i>: 
not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:132_1_1_1_2_2_1_2"/>
not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:132_1_1_1_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><b>hence </b><a NAME="E5:132_1_1_1_2_2_1_2"/>
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E19:132_1_1_1_2"/><b>then </b><i><font color="Green">E189</font></i>: 
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><b>set </b><font color="Maroon">s3</font> = <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>;<br/><a NAME="E20:132_1_1_1_2"/><i><font color="Green">E191</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><a NAME="E21:132_1_1_1_2"/><b>then </b><i><font color="Green">E192</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E22:132_1_1_1_2"/>
 <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T48">AMI_1:48</a></i>;<br/><a NAME="E23:132_1_1_1_2"/><b>then </b><i><font color="Green">E193</font></i>: 
not  <a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><i><font color="Green">E194</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <font color="Maroon">S</font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T12" target="_self">Th12</a>, , , <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
;<br/><i><font color="Green">E195</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
;<br/><a NAME="E26:132_1_1_1_2"/>
<font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font>,<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="132_1_1_1_2_5"><b>proof </b></a><div class="add">

<a NAME="E1:132_1_1_1_2_5"/><i><font color="Green">E196</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/>
<a NAME="E2:132_1_1_1_2_5"/>
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> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></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"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="132_1_1_1_2_5_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="E1:132_1_1_1_2_5_1"/><i><font color="Green">E197</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="132_1_1_1_2_5_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:132_1_1_1_2_5_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:132_1_1_1_2_5_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:132_1_1_1_2_5_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:132_1_1_1_2_5_1"/>
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></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"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:132_1_1_1_2_5"/>
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p5">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p0">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2">FUNCT_7:def 2</a><br/>


</div><b>end;</b></div><a NAME="E27:132_1_1_1_2"/><b>then </b><i><font color="Green">E198</font></i>: 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span>, <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_7.html#R1">equal_outside</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E5:132_1_1"><i><font color="Green">E57</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">k</font> = <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1, <font color="Maroon">m</font> = <font color="Maroon">m</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><i><font color="Green">E199</font></i>: <font color="Maroon">x</font> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</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="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:132_1_1_1_2"><i><font color="Green">E81</font></i></a>, <a class="txt" href="amistd_2.html#E15"><i><font color="Green">Lemma85</font></i></a>, <a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">k</font>
<b>by </b><i>, </i>
<br/>.= 
 <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"><a href="amistd_1.html#K7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p5">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p0">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="scmfsa6a.html#T29">SCMFSA6A:29</a></i>
;<br/><a NAME="E30:132_1_1_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <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"><a href="amistd_1.html#K7">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p0">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T15" target="_self">Th15</a>, , <a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>;<br/><a NAME="E31:132_1_1_1_2"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p0">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T15" target="_self">Th15</a>, </i>;<br/><a NAME="E32:132_1_1_1_2"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p0">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/><a NAME="E33:132_1_1_1_2"/><b>then </b><i><font color="Green">E200</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p0">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><b>reconsider </b><font color="Maroon">nn</font> =  <a href="amistd_1.html#K7">locnum</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="ami_5.html#K8">+*</a> <font color="Maroon">v</font></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span> <a href="ami_3.html#K14">.--&gt;</a> <span class="p5">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p0">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><a NAME="E35:132_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<font color="Maroon">k</font></span>)</span>,<font color="Maroon">k</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="amistd_2.html#D4" target="_self">Def4</a></i>;<br/><b>hence </b><a NAME="E36:132_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
