<?xml version="1.0"?>
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<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="E1:76"/>
( not <font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a> &amp; <font color="Maroon">Y</font> is <a href="finset_1.html#V1">finite</a> &amp; <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<a NAME="E2:76"/><b>then </b><i><font color="Green">E44</font></i>: 
( not  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> is <a href="finset_1.html#V1">finite</a> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 
<b>by </b><i>, <a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/>
<a NAME="E3:76"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> &amp; 0 <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> )
 
<b>by </b><i>, <a class="ref" href="ordinal3.html#T10">ORDINAL3:10</a></i>;<br/>
<a NAME="E4:76"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">X</font></span>)</span> <a href="card_2.html#K2">*`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:76"/><b>then </b>
 <a href="card_1.html#K1">Card</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">X</font></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="card_2.html#D2">CARD_2:def 2</a></i>;<br/>
<a NAME="E6:76"/><b>then </b>
 <a href="card_1.html#K1">Card</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="card_2.html#T14">CARD_2:14</a></i>;<br/>
<b>hence </b><a NAME="E7:76"/>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">X</font> <a href="wellord2.html#R2">are_equipotent</a>  &amp;  <a href="card_1.html#K1">Card</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="card_1.html#T21">CARD_1:21</a></i>;<br/>


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