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<b>let </b><font color="Maroon" title="c1">N</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="card_fil.html#D14" target="_self" title="CARD_FIL:def.14">CARD_FIL:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  implies  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> 2,<font color="Maroon" title="c1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  )</span><br/>

<b>assume </b><a NAME="E1:45"/>
<font color="Maroon" title="c1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> 2,<font color="Maroon" title="c1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> </span><br/>

<a NAME="E2:45"/><b>then </b>
<font color="Maroon" title="c1">N</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
;<br/>
<a NAME="E3:45"/><b>then </b>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">N</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
;<br/>
<a NAME="E4:45"/><b>then </b>
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> 2,<span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c1">N</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="card_2.html#T44" title="CARD_2:th.44">CARD_2:44</a></i>;<br/>
<a NAME="E5:45"/><b>then </b>
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> 2,<font color="Maroon" title="c1">N</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="card_1.html#D5" title="CARD_1:def.5">CARD_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E6:45"/>
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> 2,<font color="Maroon" title="c1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 <b>by </b><i><a class="ref" href="card_1.html#T103" title="CARD_1:th.103">CARD_1:103</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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