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<b>take </b>
 <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span> is <a href="card_1.html#V2" title="CARD_1:attr.2">limit_cardinal</a> &amp; not  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )</span><br/>

<a NAME="E1:58_1_1"/>
 <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K2" title="CARD_1:func.2">nextcard</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T39" title="CARD_1:th.39">CARD_1:39</a>, <a class="ref" href="card_1.html#T83" title="CARD_1:th.83">CARD_1:83</a></i>;<br/>
<b>hence </b><a NAME="E2:58_1_1"/>
( not  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span> is <a href="card_1.html#V2" title="CARD_1:attr.2">limit_cardinal</a> &amp; not  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )
 ; <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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