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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a>; <span class="comment"><font color="firebrick">:: according to </font></span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K4" title="ORDINAL1:func.4">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#K4" title="ORDINAL1:func.4">omega</a>  )</span><br/>

<span class="kw">assume </span><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#K4" title="ORDINAL1:func.4">omega</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K4" title="ORDINAL1:func.4">omega</a> </span><br/>

<a NAME="E2:45"/><span class="kw">then </span>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">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="E3:45"/><span class="kw">then </span>
 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T31" title="CARD_2:th.31">CARD_2:31</a></span>;<br/>
<a NAME="E4:45"/><span class="kw">then </span>
 <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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D2" title="CARD_1:def.2">CARD_1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:45"/>
 <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#K4" title="ORDINAL1:func.4">omega</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T61" title="CARD_1:th.61">CARD_1:61</a></span>; <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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