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<span class="kw">take </span>
 <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K4" title="ORDINAL1:func.4">omega</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T19" title="CARD_1:th.19">CARD_1:19</a>, <a class="ref" href="card_1.html#T46" title="CARD_1:th.46">CARD_1:46</a></span>;<br/>
<span class="kw">hence </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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