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

<b>let </b><font color="Maroon">a</font> be    <a href="ami_3.html#M1">Data-Location</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>



<b>set </b><font color="Maroon">I</font> = <font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font>;<br/>
<b>thus </b><a NAME="E1:73"/>
 <a href="ami_7.html#K4" target="_self">Out_U_Inp</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="tarski.html#K2">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">o</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:73_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="ami_7.html#K4" target="_self">Out_U_Inp</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">o</font> = <font color="Maroon">o</font> as   <a href="ami_1.html#NM1">Object</a> of <a href="ami_3.html#K1">SCM</a>  ;<br/>
<b>consider </b><font color="Maroon">s</font> being   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">w</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">o</font><b> such that </b><br/><a NAME="E4:73_1"/><i><font color="Green">E47</font></i>: 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font>
 <b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1_1"/>
( <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  or <font color="Maroon">o</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  or ( <font color="Maroon">o</font> is    <a href="ami_3.html#M1">Data-Location</a>  &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font> ) or ( <font color="Maroon">o</font> is    <a href="ami_3.html#M1">Data-Location</a>  &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font> ) )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T3">AMI_6:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:73_1_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_2"/>
<font color="Maroon">o</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:73_1_1_2"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_3"><b>suppose </b></a><a NAME="E1:73_1_1_3"/>
( <font color="Maroon">o</font> is    <a href="ami_3.html#M1">Data-Location</a>  &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:73_1_1_3"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:73_1_1_4"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">o</font> is    <a href="ami_3.html#M1">Data-Location</a> 
 <b>and </b><br/><a NAME="E2:73_1_1_4"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font>
 ;<br/><div class="add"><a NAME="E3:73_1_1_4"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_7.html#D5" target="_self">Def5</a>, <a class="ref" href="ami_5.html#T20">AMI_5:20</a></i>;<br/><a NAME="E4:73_1_1_4"/><i><font color="Green">E56</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E5:73_1_1_4"/><i><font color="Green">E57</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E6:73_1_1_4"/><i><font color="Green">E95</font></i>: 
for <font color="Olive">d</font> being   <a href="ami_3.html#M1">Data-Location</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Olive">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_4_1"><b>proof </b></a><div class="add">

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

<a NAME="E1:73_1_1_4_1"/><i><font color="Green">E96</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">d</font>
 
<b>by </b><i><a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1_1_4_1_1"/>
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font> or <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_4_1_1_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">d</font> = 
<font color="Maroon">w</font>
<b>by </b><i>, <a class="ref" href="ami_7.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ami_7.html#T11" target="_self">Th11</a>, <a class="ref" href="ami_7.html#T15" target="_self">Th15</a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_4_1_1_2"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">o</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">d</font> = 
<font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ami_7.html#T12" target="_self">Th12</a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ami_7.html#T15" target="_self">Th15</a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E7:73_1_1_4"/><i><font color="Green">E105</font></i>: 
for <font color="Olive">i</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  holds  <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Olive">i</font>
 <b>by </b><i/>;<br/><a NAME="E8:73_1_1_4"/><i><font color="Green">E106</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="ami_7.html#T9" target="_self">Th9</a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>;<br/><i><font color="Green">E107</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span>

<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_7.html#T10" target="_self">Th10</a>, </i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_1_4_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_4_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1_1_4_3_1"/>
( <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_4_3_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_4_3_1_1"/><i><font color="Green">E108</font></i>: 
<font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> = 
<font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="ami_7.html#T15" target="_self">Th15</a>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_7.html#T18" target="_self">Th18</a>, <a class="ref" href="ami_7.html#T19" target="_self">Th19</a>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_4_3_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_4_3_1_2"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>hence </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span> = 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_7.html#T15" target="_self">Th15</a>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
<br/>.= 
 <a href="ami_3.html#K11">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_7.html#T10" target="_self">Th10</a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">o</font>,<font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_7.html#T18" target="_self">Th18</a>, <a class="ref" href="ami_7.html#T19" target="_self">Th19</a>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E11:73_1_1_4"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="ami_7.html#D4" target="_self">Def4</a>, , <a class="ref" href="ami_7.html#T12" target="_self">Th12</a>, <a class="ref" href="ami_5.html#T26">AMI_5:26</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>

<b>let </b><font color="Maroon">o</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:73"/><i><font color="Green">E128</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_2"/>
( <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or <font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_2_1"><b>suppose </b></a><a NAME="E1:73_2_1"/><i><font color="Green">E129</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><a NAME="E2:73_2_1"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_5.html#T20">AMI_5:20</a></i>;<br/><b>reconsider </b><font color="Maroon">nf</font> = <font color="Maroon">f</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <b>by </b><i><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a></i>;<br/><b>set </b><font color="Maroon">q</font> = <font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font>;<br/><b>set </b><font color="Maroon">s</font> = <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1;<br/><i><font color="Green">E132</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_7.html#D5" target="_self">Def5</a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>
<br/>.= 
<font color="Maroon">nf</font>
<b>by </b><i><a class="ref" href="ami_7.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/><a NAME="E5:73_2_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E6:73_2_1"/><b>then </b><i><font color="Green">E133</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>;<br/><b>reconsider </b><font color="Maroon">w</font> = 0 as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">a</font> <b>by </b><i/>;<br/><a NAME="E8:73_2_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="ami_3.html#K1">SCM</a> 
 <b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>;<br/><a NAME="E9:73_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">a</font>,<font color="Maroon">w</font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font>
 <b>by </b><i><a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>;<br/><a NAME="E10:73_2_1"/><b>then </b><i><font color="Green">E137</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">a</font>,<font color="Maroon">w</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">a</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">a</font>,<font color="Maroon">w</font></span>)</span>

<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_7.html#D5" target="_self">Def5</a>, </i>
<br/>.= 
 <a href="ami_3.html#K11">Next</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="ami_7.html#T9" target="_self">Th9</a>, <a class="ref" href="ami_7.html#T10" target="_self">Th10</a>, <a class="ref" href="ami_3.html#T14">AMI_3:14</a></i>
;<br/><a NAME="E12:73_2_1"/><b>then </b>
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">a</font>,<font color="Maroon">w</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">t</font> <a href="ami_7.html#K1" target="_self">+*</a> <span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span>,<font color="Maroon">nf</font></span>)</span> <a href="ami_7.html#K6" target="_self">+*</a> <font color="Maroon">a</font>,1</span>)</span></span>)</span> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">a</font>,<font color="Maroon">w</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E13:73_2_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="ami_7.html#K4" target="_self">Out_U_Inp</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#D4" target="_self">Def4</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_2_2"><b>suppose </b></a><a NAME="E1:73_2_2"/><i><font color="Green">E139</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> 
 ;<br/><div class="add"><a NAME="E2:73_2_2"/><i><font color="Green">E140</font></i>: 
 <a href="ami_7.html#K2" target="_self">Output</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_7.html#K4" target="_self">Out_U_Inp</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E3:73_2_2"/>
 <a href="ami_7.html#K2" target="_self">Output</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E4:73_2_2"/><b>then </b>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="ami_7.html#K2" target="_self">Output</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E5:73_2_2"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="ami_7.html#K4" target="_self">Out_U_Inp</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="ami_3.html#K9">=0_goto</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_7.html#D4" target="_self">Def4</a>, <a class="ref" href="ami_7.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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