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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/>

<b>given </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font><b> such that </b><a NAME="E1:36_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">f</font> is <a href="funct_2.html#V3">bijective</a>
 <b>and </b><br/><a NAME="E2:36_1_1"/>
for <font color="Olive">m</font>, <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( <font color="Olive">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n</font> iff <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">m</font> <a href="amistd_1.html#R1">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D10">AMISTD_1:def 10</a><br/>

<a NAME="E3:36_1_1"/><i><font color="Green">E45</font></i>: 
 <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> <a href="tarski.html#R2">are_equipotent</a> 
 
<b>by </b><i>, <a class="ref" href="knaster.html#T13">KNASTER:13</a></i>;<br/>
<b>thus </b><a NAME="E4:36_1_1"/>
not the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> is <a href="realset1.html#V1">trivial</a>
  <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D10" target="_self">AMISTD_2:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:36_1_1_1"/>
the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> is <a href="realset1.html#V1">trivial</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">a</font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">S</font> as  <a href="realset1.html#V1">trivial</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E3:36_1_1_1"/>
<font color="Maroon">a</font> is <a href="finset_1.html#V1">finite</a>
 
;<br/>
<b>hence </b><a NAME="E4:36_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="card_1.html#T68">CARD_1:68</a></i>;<br/>


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


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