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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <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> <font color="Maroon" title="c1">A</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a></span><br/>

<a NAME="E1:3"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E2:3"/><b>then </b>
 <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="card_1.html#T43" title="CARD_1:th.43">CARD_1:43</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="E3:3"/>
not  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c1">A</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="card_3.html#T102" title="CARD_3:th.102">CARD_3:102</a></i>; <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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