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

<a NAME="E1:8"/>
( ( <font color="Maroon">M</font> is <a href="finset_1.html#V1">finite</a> implies <font color="Maroon">M</font> <a href="hidden.html#R2">in</a>  <a href="card_1.html#K3">alef</a> 0 ) &amp; ( <font color="Maroon">M</font> <a href="hidden.html#R2">in</a>  <a href="card_1.html#K3">alef</a> 0 implies <font color="Maroon">M</font> is <a href="finset_1.html#V1">finite</a> ) &amp; ( <font color="Maroon">M</font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K3">alef</a> 0 implies  not  <a href="card_1.html#K3">alef</a> 0 <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">M</font> ) &amp; ( not  <a href="card_1.html#K3">alef</a> 0 <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">M</font> implies <font color="Maroon">M</font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K3">alef</a> 0 ) )
 
<b>by </b><i>, <a class="ref" href="card_1.html#T14">CARD_1:14</a>, <a class="ref" href="card_1.html#T83">CARD_1:83</a></i>;<br/>
<b>hence </b><a NAME="E2:8"/>
( not <font color="Maroon">M</font> is <a href="finset_1.html#V1">finite</a> iff  <a href="card_1.html#K3">alef</a> 0 <a href="ordinal1.html#R1">c=</a> <font color="Maroon">M</font> )
 ;<br/>


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