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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#K3" title="AMI_2:func.3">SCM-Memory</a> ;<br/>

<b>thus </b><a NAME="E1:19"/>
( <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-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="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  implies <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1"/><i><font color="Green" title="E7">A1</font></i>: 
<a href="ami_2.html#K7" title="AMI_2:func.7">SCM-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="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 ;<br/>

<b>assume </b><a NAME="E2:19_1"/>
<font color="Maroon" title="c1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 ;<br/>

<a NAME="E3:19_1"/><b>then </b>
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</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#K5" title="AMI_2:func.5">NAT</a>  )
 
<b>by </b><i><a class="txt" href="ami_2.html#E10"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:19_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_2.html#E1:19_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="ami_2.html#D5" target="_self" title="AMI_2:def.5">Def5</a>, <a class="ref" href="ami_2.html#T6" target="_self" title="AMI_2:th.6">Th6</a>, <a class="ref" href="numbers.html#T27" title="NUMBERS:th.27">NUMBERS:27</a></i>;<br/>


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

<b>thus </b><a NAME="E2:19"/>
( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  implies <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-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="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  )
 <b>by </b><i><a class="ref" href="ami_2.html#D5" target="_self" title="AMI_2:def.5">Def5</a></i>;<br/>


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