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<span class="kw">let </span><font color="Maroon" title="c1">M</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</a> holds  <font color="Maroon" title="c1">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">M</font>,<font color="Olive" title="b1">a</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c2">a</font>)</span><br/>



<a NAME="E1:24"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="card_5.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="card_5.html#T16" target="_self" title="CARD_5:th.16">Th25</a></span>;<br/>
<a NAME="E2:24"/><span class="kw">then </span>
( ( <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c2">a</font>) ) or (  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">M</font>,1) <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c2">a</font>) &amp;  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">M</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">M</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T27" title="CARD_2:th.27">CARD_2:27</a>, <a class="ref" href="card_2.html#T93" title="CARD_2:th.93">CARD_2:93</a>, <a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:24"/>
<font color="Maroon" title="c1">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> (<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c2">a</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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