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<b>let </b><font color="Maroon" title="c1">N</font>, <font color="Maroon" title="c2">M</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"> ( <font color="Maroon" title="c1">N</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; not <font color="Maroon" title="c2">M</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> implies ( <font color="Maroon" title="c1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c1">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font> ) )</span><br/>



<b>assume </b><a NAME="E1:115"/><i><font color="Green" title="E57">Z</font></i>: 
( <font color="Maroon" title="c1">N</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; not <font color="Maroon" title="c2">M</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</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">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c1">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font> )</span><br/>

<a NAME="E2:115"/><b>then </b>
( <font color="Maroon" title="c1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  &amp;  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font> )
 
<b>by </b><i><a class="ref" href="card_3.html#T102" target="_self" title="CARD_3:th.102">Th8</a>, <a class="ref" href="card_1.html#T103" title="CARD_1:th.103">CARD_1:103</a></i>;<br/>
<b>hence </b><a NAME="E3:115"/>
<font color="Maroon" title="c1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font></span><br/>

<b>thus </b><a NAME="E4:115"/>
<font color="Maroon" title="c1">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font>
 <b>by </b><i><a class="txt" href="#E1:115"><i><font color="Green" title="E57">Z</font></i></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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