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<b>let </b><font color="Maroon">M</font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/><b>let </b><font color="Maroon">N</font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/>



<b>assume </b><a NAME="E1:32"/><i><font color="Green">E44</font></i>: 
not <font color="Maroon">M</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<a NAME="E2:32"/>
<font color="Maroon">M</font>,<font color="Maroon">N</font> <a href="xboole_0.html#R3">are_c=-comparable</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#T25">ORDINAL1:25</a></i>;<br/>
<a NAME="E3:32"/><b>then </b>
( <font color="Maroon">M</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">N</font> or <font color="Maroon">N</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D9">XBOOLE_0:def 9</a></i>;<br/>
<a NAME="E4:32"/><b>then </b>
( ( <font color="Maroon">M</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">N</font> &amp; not <font color="Maroon">N</font> is <a href="finset_1.html#V1">finite</a> ) or ( <font color="Maroon">M</font> <a href="card_2.html#K1">+`</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> &amp; <font color="Maroon">N</font> <a href="card_2.html#K1">+`</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> ) )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:32"/>
( not <font color="Maroon">M</font> <a href="card_2.html#K1">+`</a> <font color="Maroon">N</font> is <a href="finset_1.html#V1">finite</a> &amp; not <font color="Maroon">N</font> <a href="card_2.html#K1">+`</a> <font color="Maroon">M</font> is <a href="finset_1.html#V1">finite</a> )
 <b>by </b><i>, </i>;<br/>


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