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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>thus </b><a NAME="E1:53"/>
<font color="Maroon">n</font> is <a href="finset_1.html#V1">finite</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1"><b>proof </b></a><div class="add">

<a NAME="E1:53_1"/>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<b>hence </b><a NAME="E2:53_1"/>
<font color="Maroon">n</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="finset_1.html#D1">FINSET_1:def 1</a></i>;<br/>


</div><b>end;</b></div>

<b>hence </b><a NAME="E2:53"/>
 <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">n</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i/>;<br/>


</div>
