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

<b>assume </b><a NAME="E1:63"/>
<font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">X</font> = <font color="Maroon">X</font> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E3:63"/>
(  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" target="_self">card</a> <font color="Maroon">X</font></span>)</span> &amp; <font color="Maroon">X</font>, <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="wellord2.html#R2">are_equipotent</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E4:63"/><b>then </b>
(  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" target="_self">card</a> <font color="Maroon">X</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2" target="_self">nextcard</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font></span>)</span> &amp;  <a href="card_1.html#K2" target="_self">nextcard</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2" target="_self">nextcard</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:63"/>
 <a href="card_1.html#K2" target="_self">nextcard</a> <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#D1" target="_self">Def1</a></i>;<br/>


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