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<a NAME="E1:64"/><i><font color="Green">E27</font></i>: 
 <a href="ordinal1.html#K5">omega</a>  <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K4">Rank</a> <a href="ordinal1.html#K5">omega</a> 
 
<b>by </b><i><a class="ref" href="classes1.html#T44">CLASSES1:44</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">M</font> =  <a href="classes1.html#K4">Rank</a> <a href="ordinal1.html#K5">omega</a>  as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="ordinal2.html#T19">ORDINAL2:19</a></i>;<br/>
<a NAME="E3:64"/>
( <font color="Maroon">M</font> is <a href="ordinal1.html#V1">epsilon-transitive</a> &amp; <font color="Maroon">M</font> <a href="classes1.html#NR1" target="_self">is_Tarski-Class</a>  )
 
<b>by </b><i><a class="ref" href="classes2.html#T20" target="_self">Th20</a>, <a class="ref" href="classes1.html#T37">CLASSES1:37</a></i>;<br/>
<a NAME="E4:64"/><b>then </b>
( <font color="Maroon">M</font> is   <a href="classes2.html#NM1">Universe</a> &amp; <font color="Maroon">M</font> <a href="classes1.html#R1">is_Tarski-Class_of</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="classes2.html#T21" target="_self">Th21</a>, , <a class="ref" href="classes1.html#D3">CLASSES1:def 3</a>, <a class="ref" href="ordinal2.html#T19">ORDINAL2:19</a></i>;<br/>
<b>hence </b><a NAME="E5:64"/>
 <a href="classes2.html#K13" target="_self">FinSETS</a>  <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K4">Rank</a> <a href="ordinal1.html#K5">omega</a> 
 <b>by </b><i><a class="ref" href="classes1.html#D4">CLASSES1:def 4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<a NAME="E6:64"/><i><font color="Green">E28</font></i>: 
(  <a href="ordinal1.html#K3">On</a> <a href="classes2.html#K13" target="_self">FinSETS</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="ordinal1.html#K3">On</a> <a href="classes2.html#K13" target="_self">FinSETS</a>  <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  )
 
<b>by </b><i><a class="ref" href="classes2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E7:64"/><b>then </b>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K3">On</a> <a href="classes2.html#K13" target="_self">FinSETS</a> 
 
<b>by </b><i><a class="ref" href="ordinal3.html#T10">ORDINAL3:10</a></i>;<br/>
<a NAME="E8:64"/><b>then </b>
(  <a href="ordinal1.html#K5">omega</a>  <a href="ordinal1.html#R1">c=</a>  <a href="ordinal1.html#K3">On</a> <a href="classes2.html#K13" target="_self">FinSETS</a>  &amp;  <a href="classes2.html#K13" target="_self">FinSETS</a>  <a href="hidden.html#R1">=</a>  <a href="classes1.html#K4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K3">On</a> <a href="classes2.html#K13" target="_self">FinSETS</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="classes2.html#T22" target="_self">Th22</a>, <a class="ref" href="classes2.html#T4" target="_self">Th4</a>, <a class="ref" href="ordinal1.html#D12">ORDINAL1:def 12</a></i>;<br/>
<b>hence </b><a NAME="E9:64"/>
 <a href="classes1.html#K4">Rank</a> <a href="ordinal1.html#K5">omega</a>  <a href="tarski.html#R1">c=</a>  <a href="classes2.html#K13" target="_self">FinSETS</a> 
 <b>by </b><i><a class="ref" href="classes1.html#T43">CLASSES1:43</a></i>;<br/>


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