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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E1:2"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a> implies  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K3">alef</a> 0 )
 <b>by </b><i><a class="ref" href="card_1.html#T83">CARD_1:83</a>, <a class="ref" href="card_1.html#T84">CARD_1:84</a>, <a class="ref" href="card_3.html#T58">CARD_3:58</a></i>;<br/>

<b>assume </b><a NAME="E2:2"/><i><font color="Green">E4</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_1.html#K3">alef</a> 0
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> as   <a href="ordinal1.html#NM2">Ordinal</a> ;<br/>
<a NAME="E4:2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="card_4.html#E2:2"><i><font color="Green">E4</font></i></a>, <a class="ref" href="card_1.html#T83">CARD_1:83</a></i>;<br/>
<b>hence </b><a NAME="E5:2"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="card_4.html#T1" target="_self">Th1</a></i>;<br/>


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