<?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>set </b><font color="Maroon">I</font> = <font color="Maroon">a</font> <a href="ami_3.html#K3">:=</a> <font color="Maroon">a</font>;<br/>
<b>thus </b><a NAME="E1:66"/>
 <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#K3">:=</a> <font color="Maroon">a</font></span>)</span> <a href="tarski.html#R1">c=</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>
  <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="66_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="E1:66_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#K3">:=</a> <font color="Maroon">a</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="E4:66_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#K3">:=</a> <font color="Maroon">a</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#K3">:=</a> <font color="Maroon">a</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><a class="ref" href="ami_7.html#D2" target="_self">Def2</a>, </i>;<br/>
<a NAME="E5:66_1"/><i><font color="Green">E51</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="E6:66_1"/><i><font color="Green">E52</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#K3">:=</a> <font color="Maroon">a</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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:66_1_1"/>
not <font color="Maroon">o</font> <a href="hidden.html#R2">in</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>
 ;<br/><a NAME="E2:66_1_1"/><b>then </b>
<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="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:66_1_1"/><b>then </b><i><font color="Green">E53</font></i>: 
 <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#K3">:=</a> <font color="Maroon">a</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="hidden.html#R1">=</a>  <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#K3">:=</a> <font color="Maroon">a</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/>;<br/><a NAME="E4:66_1_1"/><i><font color="Green">E56</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#K3">:=</a> <font color="Maroon">a</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#K3">:=</a> <font color="Maroon">a</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="66_1_1_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/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_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="E1:66_1_1_1_1"/>
( ( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <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#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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">a</font> &amp; <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">a</font> &amp; <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="66_1_1_1_1_1"><b>suppose </b></a><b>that </b><a NAME="E1:66_1_1_1_1_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E2:66_1_1_1_1_1"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/><div class="add"><b>thus </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#K3">:=</a> <font color="Maroon">a</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> = 
<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>
<b>by </b><i>, <a class="ref" href="ami_3.html#T8">AMI_3:8</a></i>
<br/>.= 
<font color="Maroon">w</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:66_1_1_1_1_1"><i><font color="Green">E57</font></i></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#K3">:=</a> <font color="Maroon">a</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="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_1_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:66_1_1_1_1_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E2:66_1_1_1_1_2"/><i><font color="Green">E99</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>thus </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#K3">:=</a> <font color="Maroon">a</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> = 
<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>
<b>by </b><i>, <a class="ref" href="ami_3.html#T8">AMI_3:8</a></i>
<br/>.= 
<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="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#K3">:=</a> <font color="Maroon">a</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#T8">AMI_3:8</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#K3">:=</a> <font color="Maroon">a</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="funct_7.html#T34">FUNCT_7:34</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_1_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:66_1_1_1_1_3"/><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">a</font>
 <b>and </b><br/><a NAME="E2:66_1_1_1_1_3"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>
 ;<br/><div class="add"><b>thus </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#K3">:=</a> <font color="Maroon">a</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> = 
<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#T8">AMI_3:8</a></i>
<br/>.= 
<font color="Maroon">w</font>
<b>by </b><i>, , <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#K3">:=</a> <font color="Maroon">a</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="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="66_1_1_1_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:66_1_1_1_1_4"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E2:66_1_1_1_1_4"/><i><font color="Green">E107</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>thus </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#K3">:=</a> <font color="Maroon">a</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> = 
<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#T8">AMI_3:8</a></i>
<br/>.= 
<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="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#K3">:=</a> <font color="Maroon">a</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#T8">AMI_3:8</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#K3">:=</a> <font color="Maroon">a</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="funct_7.html#T34">FUNCT_7:34</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><a NAME="E5:66_1_1"/>
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#K3">:=</a> <font color="Maroon">a</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#K3">:=</a> <font color="Maroon">a</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/><b>hence </b><a NAME="E6:66_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E4:66_1_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="ami_7.html#D3" target="_self">Def3</a>, , <a class="ref" href="ami_5.html#T26">AMI_5:26</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:66_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</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>
 ;<br/>


</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="E2:66"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</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>
 ;<br/>

<a NAME="E3:66"/><b>then </b>
<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> 
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:66"/>
<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#K3">:=</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i/>;<br/>


</div>
