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<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:36"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:36"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="wellord2.html#R2">are_equipotent</a> 
 <b>by </b><i><a class="ref" href="card_1.html#T74">CARD_1:74</a></i>;<br/>
<a NAME="E4:36"/>
<font color="Maroon">c<sub>3</sub></font> <a href="ordinal1.html#R1">c=</a>  <a href="ordinal1.html#K5">omega</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>
<a NAME="E5:36"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font> <a href="card_1.html#NR1" 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_4.html#E3:36"><i><font color="Green">E26</font></i></a>, <a class="ref" href="card_1.html#T21">CARD_1:21</a>, <a class="ref" href="card_1.html#T27">CARD_1:27</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR1" 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></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="card_4.html#D1" target="_self">CARD_4:def 1</a><br/>


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