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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:21"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:21"/>
( <font color="Maroon">X</font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">Y</font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="wellord2.html#R2">are_equipotent</a>  &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>
<a NAME="E3:21"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="card_1.html#K1">Card</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">x</font>,<font color="Maroon">y</font>) <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">H<sub>4</sub></font>( <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>, <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font>,<font color="Maroon">x</font>,<font color="Maroon">y</font>)
 
<b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E4:21"/>
<span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">X</font></span>)</span> <a href="card_2.html#K1" target="_self">+`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Y</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 <b>by </b><i>, , </i>;<br/>


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