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<b>let </b><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Memory</a> ;<br/>

<b>thus </b><a NAME="E1:14"/>
( <a href="scmpds_1.html#K2" title="SCMPDS_1:func.2">SCMPDS-OK</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  implies <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:14_1"/><i><font color="Green" title="E10">A1</font></i>: 
<a href="scmpds_1.html#K2" title="SCMPDS_1:func.2">SCMPDS-OK</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 ;<br/>

<b>assume </b><a NAME="E2:14_1"/><i><font color="Green" title="E11">A2</font></i>: 
not <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:14_1_1"/>
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  or <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a>  )
 </span><b>by </b><i><a class="txt" href="scmpds_1.html#E2:14_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="scmpds_1.html#T14" target="_self" title="SCMPDS_1:th.14">Th14</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_1"><b>suppose </b></a><a NAME="E1:14_1_1_1"/>
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:14_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_1.html#E1:14_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="scmpds_1.html#D4" target="_self" title="SCMPDS_1:def.4">Def4</a>, <a class="ref" href="ami_2.html#T6" title="AMI_2:th.6">AMI_2:6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="14_1_1_2"><b>suppose </b></a><a NAME="E1:14_1_1_2"/>
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr-Loc</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:14_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_1.html#E1:14_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="scmpds_1.html#D4" target="_self" title="SCMPDS_1:def.4">Def4</a>, <a class="ref" href="scmpds_1.html#T17" target="_self" title="SCMPDS_1:th.17">Th17</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<b>thus </b><a NAME="E2:14"/>
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">SCM-Data-Loc</a>  implies <a href="scmpds_1.html#K2" title="SCMPDS_1:func.2">SCMPDS-OK</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  )
 <b>by </b><i><a class="ref" href="scmpds_1.html#D4" target="_self" title="SCMPDS_1:def.4">Def4</a></i>;<br/>


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