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<b>let </b><font color="Maroon" title="c2">a</font> be    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> ;<br/>

<b>set </b><font color="Maroon" title="c3">I</font> = <font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font>;<br/>
<b>assume </b><a NAME="E1:45"/>
not  <a href="ami_7.html#K3" title="AMI_7:func.3">Out_\_Inp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">o</font> being   <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> <b> such that </b><br/><a NAME="E3:45"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_7.html#K3" title="AMI_7:func.3">Out_\_Inp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="subset_1.html#T10" title="SUBSET_1:th.10">SUBSET_1:10</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1"/>
( <font color="Maroon" title="c4">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="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  or <font color="Maroon" title="c4">o</font> is    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a>  )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T3" title="AMI_6:th.3">AMI_6:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1"><b>suppose </b></a><a NAME="E1:45_1_1"/>
<font color="Maroon" title="c4">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="E2:45_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="ami_7.html#T23" target="_self" title="AMI_7:th.23">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_2"><b>suppose </b></a><a NAME="E1:45_1_2"/>
<font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c5">l</font> = <font color="Maroon" title="c4">o</font> as    <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>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/><a NAME="E3:45_1_2"/>
<font color="Maroon" title="c5">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o</font>
 ;<br/><b>hence </b><a NAME="E4:45_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="ami_7.html#T22" target="_self" title="AMI_7:th.22">Th22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3"><b>suppose </b></a><a NAME="E1:45_1_3"/>
<font color="Maroon" title="c4">o</font> is    <a href="ami_3.html#M1" title="AMI_3:mode.1">Data-Location</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c5">o</font> = <font color="Maroon" title="c4">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="c6">w</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 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="c5">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="c7">s</font> = <font color="Maroon" title="c1">t</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_1_3_1"/>
( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> or <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3_1_1"><b>suppose </b></a><a NAME="E1:45_1_3_1_1"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 ;<br/><div class="add"><a NAME="E2:45_1_3_1_1"/><b>then </b><i><font color="Green" title="E31">A3</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"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>;<br/><a NAME="E3:45_1_3_1_1"/><i><font color="Green" title="E32">A4</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"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span>,<font color="Maroon" title="c1">t</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:45_1_3_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>;<br/><a NAME="E4:45_1_3_1_1"/><i><font color="Green" title="E33">A5</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"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="ami_7.html#E1:45_1_3_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="txt" href="ami_7.html#E2:45_1_3_1_1"><i><font color="Green" title="E31">A3</font></i></a>, <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/><a NAME="E5:45_1_3_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 ;<br/><b>hence </b><a NAME="E6:45_1_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="ami_7.html#E3:45_1_3_1_1"><i><font color="Green" title="E32">A4</font></i></a>, <a class="txt" href="ami_7.html#E4:45_1_3_1_1"><i><font color="Green" title="E33">A5</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self" title="AMI_7:def.4">Def4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_3_1_2"><b>suppose </b></a><a NAME="E1:45_1_3_1_2"/><i><font color="Green" title="E30">A6</font></i>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 ;<br/><div class="add"><a NAME="E2:45_1_3_1_2"/><b>then </b><i><font color="Green" title="E31">A7</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"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span>,<font color="Maroon" title="c1">t</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 0
 <b>by </b><i><a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</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"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:45_1_3_1_2"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="ami_3.html#T8" title="AMI_3:th.8">AMI_3:8</a></i>
<br/>.= 
<font color="Maroon" title="c6">w</font>
<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/><a NAME="E4:45_1_3_1_2"/><b>then </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"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span>,<font color="Maroon" title="c1">t</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font> <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"><font color="Maroon" title="c2">a</font> <a href="ami_3.html#K3" title="AMI_3:func.3">:=</a> <font color="Maroon" title="c2">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">t</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">w</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <font color="Maroon" title="c5">o</font>
 <b>by </b><i><a class="txt" href="ami_7.html#E2:45_1_3_1_2"><i><font color="Green" title="E31">A7</font></i></a></i>;<br/><b>hence </b><a NAME="E5:45_1_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self" title="AMI_7:def.4">Def4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

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