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<b>let </b><font color="Maroon">X1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y2</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:13"/>
( <font color="Maroon">X1</font>,<font color="Maroon">Y1</font> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">X2</font>,<font color="Maroon">Y2</font> <a href="wellord2.html#R2">are_equipotent</a>  )
 ;<br/>

<a NAME="E2:13"/><b>then </b>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">X2</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">X1</font></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">X2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Y1</font>,<font color="Maroon">Y2</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">Y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">Y2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">X1</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y1</font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">X2</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y2</font> )
 
<b>by </b><i>, <a class="ref" href="card_1.html#T21">CARD_1:21</a></i>;<br/>
<b>hence </b><a NAME="E3:13"/>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">X2</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Y1</font>,<font color="Maroon">Y2</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a> 
 <b>by </b><i><a class="ref" href="wellord2.html#T22">WELLORD2:22</a></i>;<br/>

<b>hence </b><a NAME="E4:13"/>
 <a href="card_1.html#K1">Card</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X1</font>,<font color="Maroon">X2</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Y1</font>,<font color="Maroon">Y2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="card_1.html#T21">CARD_1:21</a></i>;<br/>


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