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<b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> non <a href="ami_1.html#V2" title="AMI_1:attr.2">void</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/>

<b>given </b><font color="Maroon" title="c3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font><b> such that </b><a NAME="E1:36_1_1"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 <b>and </b><br/><a NAME="E2:36_1_1"/>
for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/> ( <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">n</font> iff <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m</font> <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">n</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D10" title="AMISTD_1:def.10">AMISTD_1:def 10</a><br/>

<a NAME="E3:36_1_1"/><i><font color="Green" title="E27">A2</font></i>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="txt" href="amistd_2.html#E1:36_1_1"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="knaster.html#T13" title="KNASTER:th.13">KNASTER:13</a></i>;<br/>
<b>thus </b><a NAME="E4:36_1_1"/>
not the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
  <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_2.html#D10" target="_self" title="AMISTD_2:def.10">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" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">a</font> = the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instruction-Locations</a> of <font color="Maroon" title="c2">S</font> as  <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E3:36_1_1_1"/>
<font color="Maroon" title="c4">a</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
;<br/>
<b>hence </b><a NAME="E4:36_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:36_1_1"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="card_1.html#T68" title="CARD_1:th.68">CARD_1:68</a></i>;<br/>


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


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