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<a NAME="E1:63"/><i><font color="Green" title="E48">A1</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 
;<br/>
<a NAME="E2:63"/><i><font color="Green" title="E49">A2</font></i>: 
 <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 
<b>by </b><i><a class="ref" href="classes1.html#T44" title="CLASSES1:th.44">CLASSES1:44</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c1">M</font> =  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E4:63"/>
( <font color="Maroon" title="c1">M</font> is <a href="ordinal1.html#V1" title="ORDINAL1:attr.1">epsilon-transitive</a> &amp; <font color="Maroon" title="c1">M</font> is <a href="classes1.html#V2" title="CLASSES1:attr.2">Tarski</a> )
 
<b>by </b><i><a class="ref" href="classes2.html#T70" target="_self" title="CLASSES2:th.70">Th70</a></i>;<br/>
<a NAME="E5:63"/><b>then </b>
( <font color="Maroon" title="c1">M</font> is   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a> &amp; <font color="Maroon" title="c1">M</font> <a href="classes1.html#R1" title="CLASSES1:pred.1">is_Tarski-Class_of</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="#E1:63"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="#E2:63"><i><font color="Green" title="E49">A2</font></i></a>, <a class="ref" href="classes1.html#D3" title="CLASSES1:def.3">CLASSES1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:63"/>
 <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 <b>by </b><i><a class="ref" href="classes1.html#D4" title="CLASSES1:def.4">CLASSES1:def 4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a> </span><br/>

<a NAME="E7:63"/><i><font color="Green" title="E50">A3</font></i>: 
(  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  is <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">limit_ordinal</a> )
 
<b>by </b><i><a class="ref" href="classes2.html#T55" target="_self" title="CLASSES2:th.55">Th55</a></i>;<br/>
<a NAME="E8:63"/><b>then </b>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a> 
 
<b>by </b><i><a class="ref" href="ordinal3.html#T10" title="ORDINAL3:th.10">ORDINAL3:10</a></i>;<br/>
<a NAME="E9:63"/><b>then </b>
(  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  &amp;  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K3" title="ORDINAL1:func.3">On</a> <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="#E7:63"><i><font color="Green" title="E50">A3</font></i></a>, <a class="ref" href="classes2.html#T54" target="_self" title="CLASSES2:th.54">Th54</a>, <a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></i>;<br/>
<b>hence </b><a NAME="E10:63"/>
 <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a> 
 <b>by </b><i><a class="ref" href="classes1.html#T43" title="CLASSES1:th.43">CLASSES1:43</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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