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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>



<a NAME="E1:18"/><i><font color="Green" title="E15">A1</font></i>: 
( <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font></span>)</span>,<font color="Maroon">H<sub>3</sub></font>( <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font>, <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font>) <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  &amp; <font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>) <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  )
 
<b>by </b><i><a class="txt" href="card_2.html#E8"><i><font color="Green" title="E3">Lm1</font></i></a></i>;<br/>
<a NAME="E2:18"/>
( <font color="Maroon" title="c1">A</font>, <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  &amp; <font color="Maroon" title="c2">B</font>, <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font> &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 
<b>by </b><i><a class="ref" href="card_1.html#D5" title="CARD_1:def.5">CARD_1:def 5</a></i>;<br/>
<a NAME="E3:18"/><b>then </b>
( <font color="Maroon">H<sub>3</sub></font>( <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font>, <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font>),<span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>),<font color="Maroon">H<sub>3</sub></font>( <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font>, <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font>) <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  )
 
<b>by </b><i><a class="txt" href="card_2.html#E8"><i><font color="Green" title="E3">Lm1</font></i></a>, <a class="ref" href="card_2.html#T23" target="_self" title="CARD_2:th.23">Th23</a></i>;<br/>
<a NAME="E4:18"/><b>then </b>
<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>),<span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="wellord2.html#T22" title="WELLORD2:th.22">WELLORD2:22</a></i>;<br/>
<a NAME="E5:18"/><b>then </b>
( <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p2">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a>  )
 
<b>by </b><i><a class="txt" href="card_2.html#E1:18"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="wellord2.html#T22" title="WELLORD2:th.22">WELLORD2:22</a></i>;<br/>
<b>hence </b><a NAME="E6:18"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">A</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <font color="Maroon" title="c2">B</font></span>)</span>
 <b>by </b><i><a class="ref" href="card_1.html#T21" title="CARD_1:th.21">CARD_1:21</a></i>;<br/>


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