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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:3_1"/>
<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="E3:3_1"/>
 <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"><a href="card_1.html#K4">card</a> <font color="Maroon">X'</font></span>)</span>
 <b>by </b><i><a class="ref" href="card_1.html#D11">CARD_1:def 11</a></i>;<br/><b>hence </b><a NAME="E4:3_1"/>
 ex <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st  <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="Olive">n</font>
 ;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><a NAME="E2:3"/><i><font color="Green">E44</font></i>: 
 <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">n</font>
 ;<br/>

<b>thus </b><a NAME="E3:3"/>
<font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i>, </i>;<br/>


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