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<b>consider </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><br/><a NAME="E2:47_1_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">f</font> is <a href="funct_2.html#V3">bijective</a> &amp; ( 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" target="_self">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> ) ) )
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">k</font> = <font color="Maroon">k</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">k</font>
;<br/>

<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E4:47_1_1"/>
( <font color="Maroon">f</font> is <a href="funct_2.html#V3">bijective</a> &amp; ( 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" target="_self">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> ) ) &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> )
 <b>by </b><i/>;<br/>


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