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<b>let </b><font color="Maroon" title="c2">M</font>, <font color="Maroon" title="c3">N</font>, <font color="Maroon" title="c4">K</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</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="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp; not <font color="Maroon" title="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">N</font> ) or <font color="Maroon" title="c4">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or (  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">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="c4">K</font>,<font color="Maroon" title="c3">N</font> &amp;  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c4">K</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="c3">N</font>,<font color="Maroon" title="c4">K</font> ) )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:59"/><i><font color="Green" title="E44">A1</font></i>: 
( <font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c2">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">N</font> )
 <b>and </b><br/><a NAME="E2:59"/><i><font color="Green" title="E45">A2</font></i>: 
<font color="Maroon" title="c4">K</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">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="c4">K</font>,<font color="Maroon" title="c3">N</font> &amp;  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c4">K</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="c3">N</font>,<font color="Maroon" title="c4">K</font> )</span><br/>

<b>thus </b><a NAME="E3:59"/>
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> <font color="Maroon" title="c4">K</font>,<font color="Maroon" title="c2">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="c4">K</font>,<font color="Maroon" title="c3">N</font>
 <b>by </b><i><a class="txt" href="card_4.html#E1:59"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="card_4.html#E2:59"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="card_4.html#T70" target="_self" title="CARD_4:th.70">Th70</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c4">K</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="c3">N</font>,<font color="Maroon" title="c4">K</font></span><br/>

<a NAME="E4:59"/>
( <font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c4">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="txt" href="card_4.html#E2:59"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="card_2.html#T39" title="CARD_2:th.39">CARD_2:39</a></i>;<br/>
<b>hence </b><a NAME="E5:59"/>
 <a href="card_2.html#K3" title="CARD_2:func.3">exp</a> <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c4">K</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="c3">N</font>,<font color="Maroon" title="c4">K</font>
 <b>by </b><i><a class="txt" href="card_4.html#E1:59"><i><font color="Green" title="E44">A1</font></i></a>, <a class="ref" href="card_4.html#T19" target="_self" title="CARD_4:th.19">Th19</a>, <a class="ref" href="card_4.html#T70" target="_self" title="CARD_4:th.70">Th70</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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