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<b>let </b><font color="Maroon">M</font> be   <a href="card_5.html#NM1">Aleph</a>;<br/>

<b>assume </b><a NAME="E1:50"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">M</font> is <a href="card_fil.html#V5" target="_self">strong_limit</a>
 ;<br/>

<b>assume </b><a NAME="E2:50"/>
not <font color="Maroon">M</font> is <a href="card_1.html#V2">limit</a>
 ;<br/>

<b>then consider </b><font color="Maroon">N</font> being   <a href="card_1.html#NM1">Cardinal</a><b> such that </b><br/><a NAME="E4:50"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">M</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">N</font>
 <b>by </b><i><a class="ref" href="card_1.html#D7">CARD_1:def 7</a></i>;<br/>
<a NAME="E5:50"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">N</font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">M</font>
 
<b>by </b><i>, <a class="ref" href="card_1.html#T32">CARD_1:32</a></i>;<br/>
<a NAME="E6:50"/>
<font color="Maroon">M</font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_2.html#K3">exp</a> 2,<font color="Maroon">N</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:50"/><b>then </b>
not  <a href="card_2.html#K3">exp</a> 2,<font color="Maroon">N</font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="card_1.html#T14">CARD_1:14</a></i>;<br/>
<b>hence </b><a NAME="E8:50"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


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