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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c1">M</font> is <a href="card_1.html#V2" title="CARD_1:attr.2">limit</a> implies <font color="Maroon" title="c1">M</font> is <a href="card_5.html#V1" title="CARD_5:attr.1">regular</a> )</span><br/>

<b>assume </b><a NAME="E1:65_1_1"/><i><font color="Green" title="E40">A1</font></i>: 
not <font color="Maroon" title="c1">M</font> is <a href="card_1.html#V2" title="CARD_1:attr.2">limit</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">M</font> is <a href="card_5.html#V1" title="CARD_5:attr.1">regular</a></span><br/>

<b>assume </b><a NAME="E2:65_1_1"/>
not <font color="Maroon" title="c1">M</font> is <a href="card_5.html#V1" title="CARD_5:attr.1">regular</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:65_1_1"/><b>then </b>
(  <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">M</font> &amp;  <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Maroon" title="c1">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font> )
 
<b>by </b><i><a class="ref" href="card_5.html#D2" title="CARD_5:def.2">CARD_5:def 2</a>, <a class="ref" href="card_5.html#D4" title="CARD_5:def.4">CARD_5:def 4</a></i>;<br/>
<a NAME="E4:65_1_1"/><b>then </b>
 <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Maroon" title="c1">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="card_1.html#T13" title="CARD_1:th.13">CARD_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:65_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="card_fil.html#E1:65_1_1"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="card_5.html#T40" title="CARD_5:th.40">CARD_5:40</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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