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<b>consider </b><font color="Maroon" title="c5">f</font> being    <a href="ami_1.html#M6" title="AMI_1:mode.6">IL-Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c3">S</font><b> such that </b><br/><a NAME="E2:45_1_1"/><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c5">f</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> &amp; ( 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="c5">f</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</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="c5">f</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Olive" title="b2">n</font> ) ) )
 <b>by </b><i><a class="ref" href="amistd_1.html#D10" target="_self" title="AMISTD_1:def.10">Def10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">k</font> = <font color="Maroon" title="c4">k</font> as    <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>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">f</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c6">k</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c5">f</font>
;<br/>

<b>thus </b><a NAME="E4:45_1_1"/>
( <font color="Maroon" title="c5">f</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> &amp; ( 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="c5">f</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</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="c5">f</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Olive" title="b2">n</font> ) ) &amp; <font color="Maroon" title="c5">f</font> <a href="ami_1.html#K25" title="AMI_1:func.25">.</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> )
 <b>by </b><i><a class="txt" href="amistd_1.html#E2:45_1_1"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>


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