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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="E1:30"/>
( not <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> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> or  <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> ) )
 ;<br/>

<a NAME="E2:30"/><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> <a href="card_1.html#NR1" target="_self">&lt;=`</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#T13">CARD_1:13</a></i>;<br/>
<a NAME="E3:30"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:30"/><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#K1">+`</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> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <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#K1">+`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font></span>)</span> &amp;  <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> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font></span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="card_1.html#T27">CARD_1:27</a>, <a class="ref" href="card_2.html#T47">CARD_2:47</a></i>;<br/>
<a NAME="E5:30"/><b>then </b>
 <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> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E6:30"/>
( <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font>,<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">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</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><a class="ref" href="card_1.html#T21">CARD_1:21</a></i>;<br/>


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