<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>

<a NAME="E1:7"/>
( (  <a href="ordinal1.html#K5">omega</a>  <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> implies  not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a>  ) &amp; ( not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a>  implies  <a href="ordinal1.html#K5">omega</a>  <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a> implies <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a>  ) &amp; ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a>  implies <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#T7" target="_self">Th7</a>, <a class="ref" href="ordinal1.html#T7">ORDINAL1:7</a>, <a class="ref" href="ordinal1.html#T26">ORDINAL1:26</a></i>;<br/>
<b>hence </b><a NAME="E2:7"/>
( not <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a> iff  <a href="ordinal1.html#K5">omega</a>  <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>


</div>
