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<span class="kw">let </span><font color="Maroon" title="c1">a</font> be   <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">a</font> implies <font color="Maroon" title="c1">a</font> is  <a href="card_1.html#V2" title="CARD_1:attr.2">limit_cardinal</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
 <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">a</font> is  <a href="card_1.html#V2" title="CARD_1:attr.2">limit_cardinal</a> </span><br/>

<span class="kw">given </span><font color="Maroon" title="c2">M</font> being   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a><span class="kw"> such that </span><a NAME="E3:50"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<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>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:50"/>
 <a href="card_5.html#K1" title="CARD_5:func.1">cf</a> <font color="Maroon" title="c1">a</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="card_3.html#T108" title="CARD_3:th.108">CARD_3:108</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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> ;<br/>
<a NAME="E6:50"/>
 <a href="card_1.html#K2" title="CARD_1:func.2">nextcard</a> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_1.html#K2" title="CARD_1:func.2">nextcard</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="card_5.html#T35" target="_self" title="CARD_5:th.35">Th35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:50"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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