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<b>let </b><font color="Maroon" title="c1">M</font>, <font color="Maroon" title="c2">N</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a>;<br/>



<b>thus </b><a NAME="E1:8"/>
( <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">N</font> implies <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c2">N</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  )
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">A</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><b> such that </b><br/><a NAME="E3:8"/><i><font color="Green" title="E4">A1</font></i>: 
( <font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> &amp; ( for <font color="Olive" title="b1">C</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">C</font>,<font color="Maroon" title="c3">A</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  holds <br/><font color="Maroon" title="c3">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">C</font> ) )
 <b>by </b><i><a class="ref" href="card_1.html#D1" target="_self" title="CARD_1:def.1">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">B</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><b> such that </b><br/><a NAME="E5:8"/><i><font color="Green" title="E5">A2</font></i>: 
( <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> &amp; ( for <font color="Olive" title="b1">C</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>  st <font color="Olive" title="b1">C</font>,<font color="Maroon" title="c4">B</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  holds <br/><font color="Maroon" title="c4">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">C</font> ) )
 <b>by </b><i><a class="ref" href="card_1.html#D1" target="_self" title="CARD_1:def.1">Def1</a></i>;<br/>
<b>assume </b><a NAME="E6:8"/><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c2">N</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 ;<br/>

<a NAME="E7:8"/><b>then </b><i><font color="Green" title="E7">A4</font></i>: 
( <font color="Maroon" title="c4">B</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c1">M</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  )
 
<b>by </b><i><a class="txt" href="card_1.html#E3:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="card_1.html#E5:8"><i><font color="Green" title="E5">A2</font></i></a></i>;<br/>
<a NAME="E8:8"/>
<font color="Maroon" title="c3">A</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="txt" href="card_1.html#E3:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="card_1.html#E5:8"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="card_1.html#E6:8"><i><font color="Green" title="E6">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:8"/>
<font color="Maroon" title="c1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">N</font>
 <b>by </b><i><a class="txt" href="card_1.html#E3:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="card_1.html#E5:8"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="card_1.html#E7:8"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


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