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

<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">A</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Olive" title="b1">A</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">A</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><span class="kw"> such that </span><br/><a NAME="E2:72"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
 <a href="classes1.html#K1" title="CLASSES1:func.1">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5" title="CLASSES1:func.5">the_transitive-closure_of</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#T53" target="_self" title="CLASSES1:th.53">Th53</a>, <a class="ref" href="classes1.html#T58" target="_self" title="CLASSES1:th.58">Th58</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">A</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span><br/>

<a NAME="E3:72"/><span class="lab"><font color="Green" title="E50">A2</font></span>: 
 <a href="classes1.html#K5" title="CLASSES1:func.5">the_transitive-closure_of</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes1.html#K1" title="CLASSES1:func.1">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5" title="CLASSES1:func.5">the_transitive-closure_of</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#T5" target="_self" title="CLASSES1:th.5">Th5</a></span>;<br/>
<a NAME="E4:72"/><span class="lab"><font color="Green" title="E51">A3</font></span>: 
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes1.html#K1" title="CLASSES1:func.1">Tarski-Class</a> <span class="p1">(<span class="default"><a href="classes1.html#K5" title="CLASSES1:func.5">the_transitive-closure_of</a> <font color="Maroon" title="c1">X</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="classes1.html#T6" target="_self" title="CLASSES1:th.6">Th6</a>, <a class="ref" href="classes1.html#T59" target="_self" title="CLASSES1:th.59">Th59</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:72"/>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:72"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="txt" href="#E4:72"><span class="lab"><font color="Green" title="E51">A3</font></span></a>, <a class="ref" href="ordinal1.html#D2" title="ORDINAL1:def.2">ORDINAL1:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
