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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Maroon" title="c1">A</font> is   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a></span><br/>

<a NAME="E1:30"/>
<font color="Maroon" title="c1">A</font> <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#K4" title="ORDINAL1:func.4">omega</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#T23" target="_self" onmouseover="rs('abcmiz_1/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E2:30"/><span class="kw">then </span>
<font color="Maroon" title="c1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#T22" target="_self" onmouseover="rs('abcmiz_1/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<a NAME="E3:30"/><span class="kw">then </span>
 <a href="classes1.html#K6" title="CLASSES1:func.6">the_rank_of</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#T66" onmouseover="rs('classes1/T66')" onmouseout="rh()">CLASSES1:66</a></span>;<br/>
<a NAME="E4:30"/><span class="kw">then </span>
 <a href="classes1.html#K6" title="CLASSES1:func.6">the_rank_of</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Maroon" title="c1">A</font></span>)</span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#T21" target="_self" onmouseover="rs('abcmiz_1/T21')" onmouseout="rh()">Th21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:30"/>
 <a href="abcmiz_1.html#K1" title="ABCMIZ_1:func.1">varcl</a> <font color="Maroon" title="c1">A</font> is   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_1.html#T9" target="_self" onmouseover="rs('abcmiz_1/T9')" onmouseout="rh()">Th9</a>, <a class="ref" href="abcmiz_1.html#T19" target="_self" onmouseover="rs('abcmiz_1/T19')" onmouseout="rh()">Th19</a>, <a class="ref" href="abcmiz_1.html#T20" target="_self" onmouseover="rs('abcmiz_1/T20')" onmouseout="rh()">Th20</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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