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

<b>set </b><font color="Maroon" title="c5">P</font> = <font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font>;<br/>
<b>set </b><font color="Maroon" title="c6">k</font> = <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1;<br/>
<b>let </b><font color="Maroon" title="c7">f</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <font color="Maroon" title="c2">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D17" title="AMISTD_1:def.17">AMISTD_1:def 17</a><br/>

<b>assume </b><a NAME="E1:132_1_1"/><i><font color="Green" title="E72">A1</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 ;<br/>

<a NAME="E2:132_1_1"/><i><font color="Green" title="E73">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E83"><i><font color="Green" title="E67">Lm10</font></i></a></i>;<br/>
<a NAME="E3:132_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_2.html#T50" target="_self" title="AMISTD_2:th.50">Th50</a></i>;<br/>
<a NAME="E4:132_1_1"/><b>then </b><i><font color="Green" title="E74">A3</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E5:132_1_1"/><i><font color="Green" title="E75">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E6:132_1_1"/><i><font color="Green" title="E76">A5</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive" title="b1">m</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  :  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E7:132_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>,<font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c9">s2</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E9:132_1_1"/><i><font color="Green" title="E77">A6</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c9">s2</font></span>)</span>
 <b>and </b><br/><a NAME="E10:132_1_1"/><i><font color="Green" title="E78">A7</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c9">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font>
 <b>and </b><br/><a NAME="E11:132_1_1"/><i><font color="Green" title="E79">A8</font></i>: 
<font color="Maroon" title="c9">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>,<font color="Maroon" title="c7">f</font>
 ;<br/>
<a NAME="E12:132_1_1"/><i><font color="Green" title="E80">A9</font></i>: 
 <a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>,<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E1:132_1_1"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="ami_5.html#D5" title="AMI_5:def.5">AMI_5:def 5</a></i>;<br/>
<a NAME="E13:132_1_1"/><i><font color="Green" title="E81">A10</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>,<font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c9">s2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E9:132_1_1"><i><font color="Green" title="E77">A6</font></i></a>, <a class="txt" href="amistd_2.html#E10:132_1_1"><i><font color="Green" title="E78">A7</font></i></a>, <a class="txt" href="amistd_2.html#E11:132_1_1"><i><font color="Green" title="E79">A8</font></i></a></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" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> or <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> )
 </span><b>by </b><i><a class="txt" href="amistd_2.html#E1:132_1_1"><i><font color="Green" title="E72">A1</font></i></a>, <a class="txt" href="amistd_2.html#E2:132_1_1"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">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" title="E82">A11</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:132_1_1_1_1"/><b>then </b><i><font color="Green" title="E83">A12</font></i>: 
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E5:132_1_1"><i><font color="Green" title="E75">A4</font></i></a>, <a class="ref" href="amistd_1.html#D17" title="AMISTD_1:def.17">AMISTD_1:def 17</a></i>;<br/><a NAME="E3:132_1_1_1_1"/>
not <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:132_1_1"><i><font color="Green" title="E74">A3</font></i></a>, <a class="txt" href="amistd_2.html#E1:132_1_1_1_1"><i><font color="Green" title="E82">A11</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>then </b><font color="Maroon" title="c9">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c7">f</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" title="AMISTD_2:func.11">CutLastLoc</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E11:132_1_1"><i><font color="Green" title="E79">A8</font></i></a>, <a class="txt" href="amistd_2.html#E12:132_1_1"><i><font color="Green" title="E80">A9</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:132_1_1_1_1"><i><font color="Green" title="E82">A11</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
 <a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E5:132_1_1"><i><font color="Green" title="E75">A4</font></i></a>, <a class="txt" href="amistd_2.html#E1:132_1_1_1_1"><i><font color="Green" title="E82">A11</font></i></a>, <a class="ref" href="ami_5.html#D5" title="AMI_5:def.5">AMI_5:def 5</a></i>
;<br/><a NAME="E5:132_1_1_1_1"/><b>then </b>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c9">s2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c7">f</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:132_1_1"><i><font color="Green" title="E78">A7</font></i></a></i>;<br/><a NAME="E6:132_1_1_1_1"/><b>then </b><i><font color="Green" title="E84">A13</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E9:132_1_1"><i><font color="Green" title="E77">A6</font></i></a>, <a class="txt" href="amistd_2.html#E2:132_1_1_1_1"><i><font color="Green" title="E83">A12</font></i></a></i>;<br/><a NAME="E7:132_1_1_1_1"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T53" target="_self" title="AMISTD_2:th.53">Th53</a></i>;<br/><b>hence </b><a NAME="E8:132_1_1_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:132_1_1_1_1"><i><font color="Green" title="E84">A13</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" title="E82">A14</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c10">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:132_1_1_1_2"/><i><font color="Green" title="E83">A15</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:132_1_1_1_2"/><i><font color="Green" title="E84">A16</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:132_1_1"><i><font color="Green" title="E76">A5</font></i></a></i>;<br/><a NAME="E5:132_1_1_1_2"/><i><font color="Green" title="E85">A17</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E4:132_1_1_1_2"><i><font color="Green" title="E84">A16</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><a NAME="E6:132_1_1_1_2"/><b>then </b><i><font color="Green" title="E86">A18</font></i>: 
 <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#D17" title="AMISTD_1:def.17">AMISTD_1:def 17</a></i>;<br/><a NAME="E7:132_1_1_1_2"/><i><font color="Green" title="E87">A19</font></i>: 
 <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="ami_1.html#D11" title="AMI_1:def.11">AMI_1:def 11</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c11">v</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c2">S</font> <b>by </b><i><a class="ref" href="ami_1.html#T59" title="AMI_1:th.59">AMI_1:59</a></i>;<br/><b>set </b><font color="Maroon" title="c12">s1</font> = <font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font>;<br/><i><font color="Green" title="E88">A20</font></i>:  <a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>,<font color="Maroon" title="c7">f</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E12:132_1_1"><i><font color="Green" title="E80">A9</font></i></a>, <a class="txt" href="amistd_2.html#E1:132_1_1_1_2"><i><font color="Green" title="E82">A14</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:132_1_1_1_2"><i><font color="Green" title="E83">A15</font></i></a>, <a class="txt" href="amistd_2.html#E4:132_1_1_1_2"><i><font color="Green" title="E84">A16</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self" title="AMISTD_2:def.16">Def16</a></i>
;<br/><a NAME="E10:132_1_1_1_2"/><i><font color="Green" title="E89">A21</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>;<br/><a NAME="E11:132_1_1_1_2"/><i><font color="Green" title="E90">A22</font></i>: 
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E12:132_1_1_1_2"/><i><font color="Green" title="E91">A23</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/><a NAME="E13:132_1_1_1_2"/><i><font color="Green" title="E92">A24</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:132_1_1_1_2"><i><font color="Green" title="E89">A21</font></i></a>, <a class="txt" href="amistd_2.html#E11:132_1_1_1_2"><i><font color="Green" title="E90">A22</font></i></a>, <a class="txt" href="amistd_2.html#E12:132_1_1_1_2"><i><font color="Green" title="E91">A23</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>;<br/><a NAME="E14:132_1_1_1_2"/><i><font color="Green" title="E93">A25</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c9">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">w</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c2">S</font> <b>by </b><i><a class="txt" href="amistd_2.html#E7:132_1_1_1_2"><i><font color="Green" title="E87">A19</font></i></a>, <a class="ref" href="ami_1.html#T59" title="AMI_1:th.59">AMI_1:59</a></i>;<br/><a NAME="E16:132_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c13">w</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">S</font>
 ;<br/><a NAME="E17:132_1_1_1_2"/><b>then </b><i><font color="Green" title="E94">A26</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a></i>;<br/><a NAME="E18:132_1_1_1_2"/>
for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c9">s2</font> holds <br/><font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">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" title="c14">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:132_1_1_1_2_2"/>
<font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c9">s2</font>
 ;<br/>

<a NAME="E2:132_1_1_1_2_2"/><i><font color="Green" title="E95">A27</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">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" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font> or <font color="Maroon" title="c14">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">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" title="E96">A28</font></i>: 
<font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font>
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> = 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E10:132_1_1"><i><font color="Green" title="E78">A7</font></i></a>, <a class="txt" href="amistd_2.html#E3:132_1_1_1_2"><i><font color="Green" title="E83">A15</font></i></a>, <a class="txt" href="amistd_2.html#E13:132_1_1_1_2"><i><font color="Green" title="E92">A24</font></i></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">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" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:132_1_1_1_2_2_1_1"><i><font color="Green" title="E96">A28</font></i></a>, <a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E11:132_1_1_1_2"><i><font color="Green" title="E90">A22</font></i></a>, <a class="txt" href="amistd_2.html#E2:132_1_1_1_2_2"><i><font color="Green" title="E95">A27</font></i></a>, <a class="txt" href="amistd_2.html#E1:132_1_1_1_2_2_1_1"><i><font color="Green" title="E96">A28</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">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" title="E96">A29</font></i>: 
<font color="Maroon" title="c14">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font>
 ;<br/><div class="add"><a NAME="E2:132_1_1_1_2_2_1_2"/><b>then </b><i><font color="Green" title="E97">A30</font></i>: 
not <font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:132_1_1_1_2_2"><i><font color="Green" title="E95">A27</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:132_1_1_1_2_2_1_2"/>
not <font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E12:132_1_1_1_2"><i><font color="Green" title="E91">A23</font></i></a>, <a class="txt" href="amistd_2.html#E1:132_1_1_1_2_2_1_2"><i><font color="Green" title="E96">A29</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><b>hence </b><a NAME="E5:132_1_1_1_2_2_1_2"/>
<font color="Maroon" title="c9">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">a</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:132_1_1_1_2_2_1_2"><i><font color="Green" title="E97">A30</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">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" title="E95">A31</font></i>: 
<font color="Maroon" title="c9">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E14:132_1_1_1_2"><i><font color="Green" title="E93">A25</font></i></a>, <a class="txt" href="amistd_2.html#E17:132_1_1_1_2"><i><font color="Green" title="E94">A26</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/><b>set </b><font color="Maroon" title="c14">s3</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span>;<br/><a NAME="E20:132_1_1_1_2"/><i><font color="Green" title="E96">A32</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span><a href="realset1.html#K5" title="REALSET1:func.5">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/><a NAME="E21:132_1_1_1_2"/><b>then </b><i><font color="Green" title="E97">A33</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E22:132_1_1_1_2"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T48" title="AMI_1:th.48">AMI_1:48</a></i>;<br/><a NAME="E23:132_1_1_1_2"/><b>then </b><i><font color="Green" title="E98">A34</font></i>: 
not  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E20:132_1_1_1_2"><i><font color="Green" title="E96">A32</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><i><font color="Green" title="E99">A35</font></i>:  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c2">S</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E23:132_1_1_1_2"><i><font color="Green" title="E98">A34</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E10:132_1_1_1_2"><i><font color="Green" title="E89">A21</font></i></a>, <a class="txt" href="amistd_2.html#E11:132_1_1_1_2"><i><font color="Green" title="E90">A22</font></i></a>, <a class="txt" href="amistd_2.html#E12:132_1_1_1_2"><i><font color="Green" title="E91">A23</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
;<br/><i><font color="Green" title="E100">A36</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E21:132_1_1_1_2"><i><font color="Green" title="E97">A33</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>
;<br/><a NAME="E26:132_1_1_1_2"/>
<font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">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" title="E101">A37</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> )
 
<b>by </b><i><a class="ref" href="ami_3.html#T36" title="AMI_3:th.36">AMI_3:36</a></i>;<br/>
<a NAME="E2:132_1_1_1_2_5"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="132_1_1_1_2_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c15">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:132_1_1_1_2_5_1"/><i><font color="Green" title="E102">A38</font></i>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font>
 ;<br/>

<div><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" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p2">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">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" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E20:132_1_1_1_2"><i><font color="Green" title="E96">A32</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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="txt" href="amistd_2.html#E1:132_1_1_1_2_5_1"><i><font color="Green" title="E102">A38</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">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" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">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" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p5">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p0">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E1:132_1_1_1_2_5"><i><font color="Green" title="E101">A37</font></i></a>, <a class="ref" href="scmfsa6a.html#T9" title="SCMFSA6A:th.9">SCMFSA6A:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_7.html#D2" title="FUNCT_7:def.2">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" title="E101">A39</font></i>: 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span>, <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="ref" href="amistd_2.html#D19" target="_self" title="AMISTD_2:def.19">Def19</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">k</font> = <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1, <font color="Maroon" title="c16">m</font> = <font color="Maroon" title="c10">m</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><i><font color="Green" title="E102">A40</font></i>: <font color="Maroon" title="c8">x</font> = 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K8" title="AMISTD_2:func.8">IncAddr</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c9">s2</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E13:132_1_1"><i><font color="Green" title="E81">A10</font></i></a>, <a class="txt" href="amistd_2.html#E5:132_1_1_1_2"><i><font color="Green" title="E85">A17</font></i></a>, <a class="txt" href="amistd_2.html#E9:132_1_1_1_2"><i><font color="Green" title="E88">A20</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span></span>)</span></span>)</span> <a href="amistd_1.html#K8" title="AMISTD_1:func.8">+</a> <font color="Maroon" title="c15">k</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E19:132_1_1_1_2"><i><font color="Green" title="E95">A31</font></i></a>, <a class="ref" href="amistd_2.html#D17" target="_self" title="AMISTD_2:def.17">Def17</a></i>
<br/>.= 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p3">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p4">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p5">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p0">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c15">k</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E27:132_1_1_1_2"><i><font color="Green" title="E101">A39</font></i></a>, <a class="ref" href="scmfsa6a.html#T29" title="SCMFSA6A:th.29">SCMFSA6A:29</a></i>
;<br/><a NAME="E30:132_1_1_1_2"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p0">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E24:132_1_1_1_2"><i><font color="Green" title="E99">A35</font></i></a>, <a class="txt" href="amistd_2.html#E25:132_1_1_1_2"><i><font color="Green" title="E100">A36</font></i></a>, <a class="ref" href="amistd_1.html#D13" title="AMISTD_1:def.13">AMISTD_1:def 13</a></i>;<br/><a NAME="E31:132_1_1_1_2"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p0">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E24:132_1_1_1_2"><i><font color="Green" title="E99">A35</font></i></a>, <a class="txt" href="amistd_2.html#E25:132_1_1_1_2"><i><font color="Green" title="E100">A36</font></i></a></i>;<br/><a NAME="E32:132_1_1_1_2"/><b>then </b>
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p0">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c4">G</font>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:132_1_1_1_2"><i><font color="Green" title="E86">A18</font></i></a></i>;<br/><a NAME="E33:132_1_1_1_2"/><b>then </b><i><font color="Green" title="E103">A41</font></i>: 
 <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p2">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p4">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p5">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p0">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c15">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self" title="AMISTD_2:def.15">Def15</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c17">nn</font> =  <a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p3">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p4">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c16">m</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">s2</font> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <font color="Maroon" title="c11">v</font></span>)</span> <a href="ami_5.html#K8" title="AMI_5:func.8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p5">(<span class="default"><a href="ami_5.html#K5" title="AMI_5:func.5">pi</a> <font color="Maroon" title="c4">G</font>,<span class="p0">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/><a NAME="E35:132_1_1_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" title="AMISTD_2:func.10">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" title="AMISTD_2:func.9">IncAddr</a> <font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c15">k</font></span>)</span>,<font color="Maroon" title="c15">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:132_1_1"><i><font color="Green" title="E76">A5</font></i></a>, <a class="txt" href="amistd_2.html#E29:132_1_1_1_2"><i><font color="Green" title="E102">A40</font></i></a>, <a class="txt" href="amistd_2.html#E33:132_1_1_1_2"><i><font color="Green" title="E103">A41</font></i></a></i>;<br/><b>hence </b><a NAME="E36:132_1_1_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="amistd_2.html#K12" title="AMISTD_2:func.12">';'</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E2:132_1_1"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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