<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:55"/><i><font color="Green">E35</font></i>: 
( (  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> or  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> ) &amp; <font color="Maroon">Y</font> is <a href="finset_1.html#V1">finite</a> )
 ;<br/>

<a NAME="E2:55"/><b>then </b>
( (  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="ordinal1.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> or  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> ) &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="wellord2.html#R2">are_equipotent</a>  )
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>
<a NAME="E3:55"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="ordinal1.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> is <a href="finset_1.html#V1">finite</a> )
 
<b>by </b><i>, <a class="ref" href="card_1.html#T68">CARD_1:68</a>, <a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>
<a NAME="E4:55"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a> &amp; <font color="Maroon">X</font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="wellord2.html#R2">are_equipotent</a>  )
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:55"/>
<font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="card_1.html#T68">CARD_1:68</a></i>;<br/>


</div>
