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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>assume </b><a NAME="E1:59"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<a NAME="E2:59"/>
<font color="Maroon">c<sub>1</sub></font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="wellord2.html#R2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>
<a NAME="E3:59"/><b>then </b>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="txt" href="card_3.html#E1:59"><i><font color="Green">E27</font></i></a>, <a class="ref" href="card_1.html#T68">CARD_1:68</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:59"/><i><font color="Green">E28</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="card_1.html#T86">CARD_1:86</a></i>;<br/>
<b>thus </b><a NAME="E6:59"/>
 <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#K1">Card</a> <a href="ordinal1.html#K5">omega</a> 
 <b>by </b><i><a class="txt" href="card_3.html#E5:59"><i><font color="Green">E28</font></i></a>, <a class="ref" href="card_1.html#T84">CARD_1:84</a></i>;<br/>


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