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

<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/>



<b>set </b><font color="Maroon" title="c5">I</font> =  <a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1"><b>suppose </b></a><a NAME="E1:71_1_1"/><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 ;<br/><div class="add"><b>thus </b><a NAME="E2:71_1_1"/>
 <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">o</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="E1:71_1_1_1"/><i><font color="Green" title="E56">A2</font></i>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c7">o</font> = <font color="Maroon" title="c6">o</font> as   <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  ;<br/>
<b>consider </b><font color="Maroon" title="c8">s</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> , <font color="Maroon" title="c9">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c7">o</font><b> such that </b><br/><a NAME="E4:71_1_1_1"/><i><font color="Green" title="E57">A3</font></i>: 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="ami_7.html#D5" target="_self" title="AMI_7:def.5">Def5</a></i>;<br/>
<a NAME="E5:71_1_1_1"/><i><font color="Green" title="E58">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">s</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 <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E6:71_1_1_1"/><i><font color="Green" title="E59">A5</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</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 <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:71_1_1_1_1"/><i><font color="Green" title="E60">A6</font></i>: 
<font color="Maroon" title="c7">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 <b>and </b><br/><a NAME="E2:71_1_1_1_1"/><i><font color="Green" title="E61">A7</font></i>: 
<font color="Maroon" title="c7">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 ;<br/><b>assume </b><a NAME="E3:71_1_1_1_1"/>
<font color="Maroon" title="c7">o</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> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><a NAME="E4:71_1_1_1_1"/><b>then </b><i><font color="Green" title="E62">A8</font></i>: 
 <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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <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"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#T7" target="_self" title="AMI_7:th.7">Th7</a></i>;<br/><a NAME="E5:71_1_1_1_1"/><i><font color="Green" title="E63">A9</font></i>: 
for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  holds  <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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_1_1_1_1_1_1"/>
( <font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> or ( <font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">o</font> ) or ( <font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">o</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:71_1_1_1_1_1_1_1"/><i><font color="Green" title="E64">A10</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 ;<br/><div class="add"><b>hence </b><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_1_1"><i><font color="Green" title="E60">A6</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E2:71_1_1_1_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_1_1_1_1_1_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_1_1"><i><font color="Green" title="E60">A6</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_1_1_1_1_1_1"><i><font color="Green" title="E64">A10</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:71_1_1_1_1_1_1_2"/><i><font color="Green" title="E64">A11</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 ;<br/><div class="add"><b>hence </b><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_1_1"><i><font color="Green" title="E60">A6</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E2:71_1_1_1_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_1_1_1_1_2"><i><font color="Green" title="E64">A11</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E2:71_1_1_1_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_1_1_1_1_1_2"><i><font color="Green" title="E64">A11</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_1_1_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:71_1_1_1_1_1_1_3"/><i><font color="Green" title="E64">A12</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 <b>and </b><br/><a NAME="E2:71_1_1_1_1_1_1_3"/><i><font color="Green" title="E65">A13</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 <b>and </b><br/><a NAME="E3:71_1_1_1_1_1_1_3"/><i><font color="Green" title="E66">A14</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">o</font>
 ;<br/><div class="add"><b>thus </b><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_1_1_1_1_3"><i><font color="Green" title="E64">A12</font></i></a>, <a class="txt" href="ami_7.html#E2:71_1_1_1_1_1_1_3"><i><font color="Green" title="E65">A13</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<font color="Maroon" title="c9">w</font>
<b>by </b><i><a class="txt" href="ami_7.html#E5:71_1_1_1"><i><font color="Green" title="E58">A4</font></i></a>, <a class="txt" href="ami_7.html#E3:71_1_1_1_1_1_1_3"><i><font color="Green" title="E66">A14</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E6:71_1_1_1"><i><font color="Green" title="E59">A5</font></i></a>, <a class="txt" href="ami_7.html#E3:71_1_1_1_1_1_1_3"><i><font color="Green" title="E66">A14</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_1_1_1_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:71_1_1_1_1_1_1_4"/><i><font color="Green" title="E64">A15</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 <b>and </b><br/><a NAME="E2:71_1_1_1_1_1_1_4"/><i><font color="Green" title="E65">A16</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 <b>and </b><br/><a NAME="E3:71_1_1_1_1_1_1_4"/><i><font color="Green" title="E66">A17</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">o</font>
 ;<br/><div class="add"><b>thus </b><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_1_1_1_1_4"><i><font color="Green" title="E64">A15</font></i></a>, <a class="txt" href="ami_7.html#E2:71_1_1_1_1_1_1_4"><i><font color="Green" title="E65">A16</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E3:71_1_1_1_1_1_1_4"><i><font color="Green" title="E66">A17</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_1_1_1_1_4"><i><font color="Green" title="E64">A15</font></i></a>, <a class="txt" href="ami_7.html#E2:71_1_1_1_1_1_1_4"><i><font color="Green" title="E65">A16</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E3:71_1_1_1_1_1_1_4"><i><font color="Green" title="E66">A17</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E6:71_1_1_1_1"/>
for <font color="Olive" title="b1">i</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  holds  <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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b1">i</font>
 <b>by </b><i><a class="ref" href="ami_7.html#T8" target="_self" title="AMI_7:th.8">Th8</a></i>;<br/><b>hence </b><a NAME="E7:71_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E4:71_1_1_1"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="ami_7.html#E4:71_1_1_1_1"><i><font color="Green" title="E62">A8</font></i></a>, <a class="txt" href="ami_7.html#E5:71_1_1_1_1"><i><font color="Green" title="E63">A9</font></i></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:71_1_1_1"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>


</div><b>end;</b></div><b>let </b><font color="Maroon" title="c6">o</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="E3:71_1_1"/><i><font color="Green" title="E56">A18</font></i>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 ;<br/><div><i><font color="Green" title="E57">A19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_2"><b>now </b></a><div class="add"><a NAME="E1:71_1_1_2"/><i><font color="Green" title="E58">A20</font></i>: 
 <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#T11" target="_self" title="AMI_7:th.11">Th11</a></i>;<br/><a NAME="E2:71_1_1_2"/>
 <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="ami_7.html#T48" target="_self" title="AMI_7:th.48">Th48</a></i>;<br/><a NAME="E3:71_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:71_1_1_2"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_2"><i><font color="Green" title="E58">A20</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_1_1_3"/>
( <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  or <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 </span><b>by </b><i><a class="txt" href="ami_7.html#E3:71_1_1"><i><font color="Green" title="E56">A18</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_3_1"><b>suppose </b></a><a NAME="E1:71_1_1_3_1"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:71_1_1_3_1"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#T27" target="_self" title="AMI_7:th.27">Th27</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_3_2"><b>suppose </b></a><a NAME="E1:71_1_1_3_2"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:71_1_1_3_2"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E4:71_1_1"><i><font color="Green" title="E57">A19</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_1_3_3"><b>suppose </b></a><a NAME="E1:71_1_1_3_3"/><i><font color="Green" title="E58">A21</font></i>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c7">o</font> = <font color="Maroon" title="c6">o</font> as    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  ;<br/><b>reconsider </b><font color="Maroon" title="c8">w</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c7">o</font> <b>by </b><i><a class="txt" href="ami_7.html#E40"><i><font color="Green" title="E27">Lm2</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">w2</font> = 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c7">o</font> <b>by </b><i><a class="txt" href="ami_7.html#E40"><i><font color="Green" title="E27">Lm2</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c10">q</font> = <font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2;<br/><b>set </b><font color="Maroon" title="c11">s</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font>;<br/><a NAME="E5:71_1_1_3_3"/><i><font color="Green" title="E59">A22</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="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</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 <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/><a NAME="E6:71_1_1_3_3"/><i><font color="Green" title="E60">A23</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="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</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 <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/><i><font color="Green" title="E61">A24</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_1_3_3"><i><font color="Green" title="E58">A21</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
2
<b>by </b><i><a class="txt" href="ami_7.html#E39"><i><font color="Green" title="E26">Lm1</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
;<br/><i><font color="Green" title="E62">A25</font></i>: <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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c8">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c8">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c8">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c8">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_3_3"><i><font color="Green" title="E58">A21</font></i></a>, <a class="txt" href="ami_7.html#E5:71_1_1_3_3"><i><font color="Green" title="E59">A22</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="int_1.html#T75" title="INT_1:th.75">INT_1:75</a></i>
;<br/><span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c8">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font> = 
<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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_1_3_3"><i><font color="Green" title="E58">A21</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> 1
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_1_3_3"><i><font color="Green" title="E58">A21</font></i></a>, <a class="txt" href="ami_7.html#E6:71_1_1_3_3"><i><font color="Green" title="E60">A23</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K6" title="AMI_7:func.6">+*</a> <font color="Maroon" title="c3">a</font>,2</span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w2</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="ref" href="pre_ff.html#T2" title="PRE_FF:th.2">PRE_FF:2</a></i>
;<br/><b>hence </b><a NAME="E10:71_1_1_3_3"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E7:71_1_1_3_3"><i><font color="Green" title="E61">A24</font></i></a>, <a class="txt" href="ami_7.html#E8:71_1_1_3_3"><i><font color="Green" title="E62">A25</font></i></a>, <a class="ref" href="ami_7.html#D5" target="_self" title="AMI_7:def.5">Def5</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2"><b>suppose </b></a><a NAME="E1:71_1_2"/><i><font color="Green" title="E55">A26</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 ;<br/><div class="add"><b>thus </b><a NAME="E2:71_1_2"/>
 <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">o</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="E1:71_1_2_1"/><i><font color="Green" title="E56">A27</font></i>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c7">o</font> = <font color="Maroon" title="c6">o</font> as   <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  ;<br/>
<b>consider </b><font color="Maroon" title="c8">s</font> being   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> , <font color="Maroon" title="c9">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c7">o</font><b> such that </b><br/><a NAME="E4:71_1_2_1"/><i><font color="Green" title="E57">A28</font></i>: 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2_1"><i><font color="Green" title="E56">A27</font></i></a>, <a class="ref" href="ami_7.html#D5" target="_self" title="AMI_7:def.5">Def5</a></i>;<br/>
<a NAME="E5:71_1_2_1"/><i><font color="Green" title="E58">A29</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">s</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 <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<a NAME="E6:71_1_2_1"/><i><font color="Green" title="E59">A30</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</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 <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#T79" title="AMI_1:th.79">AMI_1:79</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:71_1_2_1_1"/><i><font color="Green" title="E60">A31</font></i>: 
<font color="Maroon" title="c7">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 <b>and </b><br/><a NAME="E2:71_1_2_1_1"/><i><font color="Green" title="E61">A32</font></i>: 
<font color="Maroon" title="c7">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 ;<br/><b>assume </b><a NAME="E3:71_1_2_1_1"/>
<font color="Maroon" title="c7">o</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> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><a NAME="E4:71_1_2_1_1"/><b>then </b><i><font color="Green" title="E62">A33</font></i>: 
 <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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <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"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#T7" target="_self" title="AMI_7:th.7">Th7</a></i>;<br/><a NAME="E5:71_1_2_1_1"/><i><font color="Green" title="E63">A34</font></i>: 
for <font color="Olive" title="b1">d</font> being   <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  holds  <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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Olive" title="b1">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_2_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">d</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_1_2_1_1_1_1"/>
( <font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or ( <font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">o</font> ) or ( <font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">o</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:71_1_2_1_1_1_1_1"/><i><font color="Green" title="E64">A35</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 ;<br/><div class="add"><b>hence </b><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2"><i><font color="Green" title="E55">A26</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2_1_1"><i><font color="Green" title="E60">A31</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c4">b</font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E2:71_1_2_1_1"><i><font color="Green" title="E61">A32</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2"><i><font color="Green" title="E55">A26</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_2_1_1_1_1_1"><i><font color="Green" title="E64">A35</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2_1_1"><i><font color="Green" title="E60">A31</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_2_1_1_1_1_1"><i><font color="Green" title="E64">A35</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_1_1_1_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:71_1_2_1_1_1_1_2"/><i><font color="Green" title="E64">A36</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 <b>and </b><br/><a NAME="E2:71_1_2_1_1_1_1_2"/><i><font color="Green" title="E65">A37</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">o</font>
 ;<br/><div class="add"><b>thus </b><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2"><i><font color="Green" title="E55">A26</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_2_1_1_1_1_2"><i><font color="Green" title="E64">A36</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<font color="Maroon" title="c9">w</font>
<b>by </b><i><a class="txt" href="ami_7.html#E5:71_1_2_1"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="ami_7.html#E2:71_1_2_1_1_1_1_2"><i><font color="Green" title="E65">A37</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E6:71_1_2_1"><i><font color="Green" title="E59">A30</font></i></a>, <a class="txt" href="ami_7.html#E2:71_1_2_1_1_1_1_2"><i><font color="Green" title="E65">A37</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_1_1_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:71_1_2_1_1_1_1_3"/><i><font color="Green" title="E64">A38</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font>
 <b>and </b><br/><a NAME="E2:71_1_2_1_1_1_1_3"/><i><font color="Green" title="E65">A39</font></i>: 
<font color="Maroon" title="c10">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">o</font>
 ;<br/><div class="add"><b>thus </b><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2"><i><font color="Green" title="E55">A26</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_2_1_1_1_1_3"><i><font color="Green" title="E64">A38</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<font color="Maroon" title="c8">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E2:71_1_2_1_1_1_1_3"><i><font color="Green" title="E65">A39</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
<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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2"><i><font color="Green" title="E55">A26</font></i></a>, <a class="txt" href="ami_7.html#E1:71_1_2_1_1_1_1_3"><i><font color="Green" title="E64">A38</font></i></a>, <a class="ref" href="ami_3.html#T12" title="AMI_3:th.12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c10">d</font>
<b>by </b><i><a class="txt" href="ami_7.html#E2:71_1_2_1_1_1_1_3"><i><font color="Green" title="E65">A39</font></i></a>, <a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E6:71_1_2_1_1"/>
for <font color="Olive" title="b1">i</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">Instruction-Location</a> of  <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  holds  <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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><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_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c8">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c7">o</font>,<font color="Maroon" title="c9">w</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b1">i</font>
 <b>by </b><i><a class="ref" href="ami_7.html#T8" target="_self" title="AMI_7:th.8">Th8</a></i>;<br/><b>hence </b><a NAME="E7:71_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E4:71_1_2_1"><i><font color="Green" title="E57">A28</font></i></a>, <a class="txt" href="ami_7.html#E4:71_1_2_1_1"><i><font color="Green" title="E62">A33</font></i></a>, <a class="txt" href="ami_7.html#E5:71_1_2_1_1"><i><font color="Green" title="E63">A34</font></i></a>, <a class="ref" href="ami_5.html#T26" title="AMI_5:th.26">AMI_5:26</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:71_1_2_1"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>


</div><b>end;</b></div><b>let </b><font color="Maroon" title="c6">o</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="E3:71_1_2"/><i><font color="Green" title="E56">A40</font></i>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 ;<br/><div><i><font color="Green" title="E57">A41</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_2_2"><b>now </b></a><div class="add"><a NAME="E1:71_1_2_2"/><i><font color="Green" title="E58">A42</font></i>: 
 <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#T11" target="_self" title="AMI_7:th.11">Th11</a></i>;<br/> <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span> = 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2"><i><font color="Green" title="E55">A26</font></i></a>, <a class="ref" href="ami_7.html#T48" target="_self" title="AMI_7:th.48">Th48</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T70" title="ENUMSET1:th.70">ENUMSET1:70</a></i>
;<br/><a NAME="E3:71_1_2_2"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K2" title="AMI_7:func.2">Output</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E4:71_1_2_2"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2_2"><i><font color="Green" title="E58">A42</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_1_2_3"/>
( <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  or <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 </span><b>by </b><i><a class="txt" href="ami_7.html#E3:71_1_2"><i><font color="Green" title="E56">A40</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_3_1"><b>suppose </b></a><a NAME="E1:71_1_2_3_1"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:71_1_2_3_1"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#T27" target="_self" title="AMI_7:th.27">Th27</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2_3_2"><b>suppose </b></a><a NAME="E1:71_1_2_3_2"/>
( <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c6">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:71_1_2_3_2"/>
<font color="Maroon" title="c6">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K4" title="AMI_7:func.4">Out_U_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7" title="AMI_3:func.7">Divide</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:71_1_2"><i><font color="Green" title="E55">A26</font></i></a>, <a class="txt" href="ami_7.html#E4:71_1_2"><i><font color="Green" title="E57">A41</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

</div>
