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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="E1:4"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="classes2.html#K13">FinSETS</a> 
 ;<br/>

<a NAME="E2:4"/>
 <a href="ordinal1.html#K5">omega</a>  <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D12">ORDINAL1:def 12</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E4:4"/><i><font color="Green">E5</font></i>: 
( <font color="Maroon">c<sub>2</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="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="neckla_2.html#E1:4"><i><font color="Green">E4</font></i></a>, <a class="ref" href="classes1.html#T35">CLASSES1:35</a>, <a class="ref" href="classes2.html#T71">CLASSES2:71</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  <b>by </b><i><a class="txt" href="neckla_2.html#E4:4"><i><font color="Green">E5</font></i></a>, <a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:4"/>
<font color="Maroon">c<sub>1</sub></font> is    <a href="subset_1.html#M1">Element</a> of  <a href="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="neckla_2.html#E4:4"><i><font color="Green">E5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:4"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>


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