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<span class="kw">let </span><font color="Maroon" title="c1">U</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">U</font> &amp;  <a href="classes1.html#K1" title="CLASSES1:func.1">Tarski-Class</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">U</font> &amp;  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">U</font> )</span><br/>

<a NAME="E1:70"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
 <a href="ordinal1.html#K2" title="ORDINAL1:func.2">On</a> <font color="Maroon" title="c1">U</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K2" title="ORDINAL1:func.2">On</a> <font color="Maroon" title="c1">U</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#T38" title="CLASSES1:th.38">CLASSES1:38</a></span>;<br/>
<a NAME="E2:70"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
 <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K2" title="ORDINAL1:func.2">On</a> <font color="Maroon" title="c1">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">U</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T50" target="_self" title="CLASSES2:th.50">Th54</a></span>;<br/>
<a NAME="E3:70"/>
 <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#K2" title="ORDINAL1:func.2">On</a> <font color="Maroon" title="c1">U</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T51" target="_self" title="CLASSES2:th.51">Th55</a>, <a class="ref" href="ordinal3.html#T8" title="ORDINAL3:th.8">ORDINAL3:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:70"/>
(  <a href="classes2.html#K13" title="CLASSES2:func.13">FinSETS</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">U</font> &amp;  <a href="classes1.html#K1" title="CLASSES1:func.1">Tarski-Class</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">U</font> &amp;  <a href="classes2.html#K16" title="CLASSES2:func.16">UNIVERSE</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">U</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:70"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="classes2.html#E75"><span class="lab"><font color="Green" title="E48">Lm6</font></span></a>, <a class="ref" href="classes2.html#T4" target="_self" title="CLASSES2:th.4">Th5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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