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<b>let </b><font color="Maroon" title="c1">M</font> be   <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</a>;<br/>

<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c1">M</font> is <a href="card_fil.html#V5" title="CARD_FIL:attr.5">strong_limit</a>
 ;<br/>

<b>assume </b><a NAME="E2:50"/>
not <font color="Maroon" title="c1">M</font> is <a href="card_1.html#V2" title="CARD_1:attr.2">limit</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">N</font> being   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a><b> such that </b><br/><a NAME="E4:50"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K2" title="CARD_1:func.2">nextcard</a> <font color="Maroon" title="c2">N</font>
 <b>by </b><i><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></i>;<br/>
<a NAME="E5:50"/><i><font color="Green" title="E36">A3</font></i>: 
<font color="Maroon" title="c2">N</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="txt" href="card_fil.html#E4:50"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="card_1.html#T32" title="CARD_1:th.32">CARD_1:32</a></i>;<br/>
<a NAME="E6:50"/>
<font color="Maroon" title="c1">M</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> 2,<font color="Maroon" title="c2">N</font>
 
<b>by </b><i><a class="txt" href="card_fil.html#E4:50"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="card_fil.html#T24" target="_self" title="CARD_FIL:th.24">Th24</a></i>;<br/>
<a NAME="E7:50"/><b>then </b>
not  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> 2,<font color="Maroon" title="c2">N</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="card_1.html#T14" title="CARD_1:th.14">CARD_1:14</a></i>;<br/>
<b>hence </b><a NAME="E8:50"/>
contradiction
 <b>by </b><i><a class="txt" href="card_fil.html#E1:50"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="card_fil.html#E5:50"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="card_fil.html#D14" target="_self" title="CARD_FIL:def.14">Def14</a></i>;<br/>


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