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

<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E31">A1</font></i>: 
 <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Maroon" title="c1">a</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c1">a</font>
 ;<br/>

<b>given </b><font color="Maroon" title="c2">M</font> being   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a><b> such that </b><a NAME="E2:42"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c1">a</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">M</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a><br/>

<a NAME="E3:42"/>
 <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Maroon" title="c1">a</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c2">M</font>
 
<b>by </b><i><a class="txt" href="card_5.html#E1:42"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="card_5.html#E2:42"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="card_4.html#T23" title="CARD_4:th.23">CARD_4:23</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">M</font> = <font color="Maroon" title="c2">M</font> as   <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</a> <b>by </b><i><a class="ref" href="card_5.html#T26" target="_self" title="CARD_5:th.26">Th26</a></i>;<br/>
<a NAME="E5:42"/>
 <a href="card_1.html#K2" title="CARD_1:func.2">nextcard</a> <font color="Maroon" title="c3">M</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a>  <a href="card_1.html#K2" title="CARD_1:func.2">nextcard</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="txt" href="card_5.html#E1:42"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="card_5.html#E2:42"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="card_5.html#T35" target="_self" title="CARD_5:th.35">Th35</a></i>;<br/>
<b>hence </b><a NAME="E6:42"/>
contradiction
 ;<br/>


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