<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">K</font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/><b>let </b><font color="Maroon">N</font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/>





<a NAME="E1:24"/><i><font color="Green">E35</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E2:24"/><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:24"/>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:24"/><b>then </b>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</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">M</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> = 
<a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 

;<br/>
<a NAME="E6:24"/><b>then </b><i><font color="Green">E40</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E7:24"/>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></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">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></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">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></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">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></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/>
<a NAME="E8:24"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</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">M</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></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="card_1.html#T58">CARD_1:58</a></i>;<br/>
<a NAME="E9:24"/><i><font color="Green">E43</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E10:24"/>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i/>;<br/>
<a NAME="E11:24"/><b>then </b>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>then </b><span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">1</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">N</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> = 
<a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 

;<br/>
<a NAME="E13:24"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E14:24"/>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></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">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></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">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></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">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></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/>
<a NAME="E15:24"/><b>then </b>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">1</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">N</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></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">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">1</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">N</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</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">M</font>,<span class="p3"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i>, , <a class="ref" href="card_1.html#T58">CARD_1:58</a>, <a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<a NAME="E16:24"/><b>then </b>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">N</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></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">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></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/>
<a NAME="E17:24"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></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">K</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</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="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</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/>
<a NAME="E18:24"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font>,<font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span> <a href="wellord2.html#R2">are_equipotent</a>  &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font> )
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a>, <a class="ref" href="wellord2.html#T22">WELLORD2:22</a></i>;<br/>
<b>hence </b><a NAME="E19:24"/>
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">M</font></span>)</span> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font> <a href="card_2.html#K1" target="_self">+`</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="card_2.html#K1" target="_self">+`</a> <font color="Maroon">N</font></span>)</span>
 <b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>


</div>
