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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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>  iff <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>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:20"/>
( <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>  )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:20_1"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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> </span><br/>

<span class="kw">assume </span><a NAME="E2:20_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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:20_1"/><span class="kw">then </span>
( <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="ami_2.html#E10"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:20_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E7">A1</font></span></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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:20"/>
( <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>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#D5" target="_self" title="AMI_2:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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