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<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c</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">w</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">d</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">z</font> be    <a href="hidden.html#M1">set</a> ;<br/>















<b>assume </b><a NAME="E1:20"/>
<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="incproj.html#R2">are_mutually_different</a> 
 ;<br/>

<a NAME="E2:20"/><b>then </b><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">w</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">w</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">w</font> )
 
<b>by </b><i><a class="ref" href="incproj.html#D6">INCPROJ:def 6</a></i>;<br/>
<b>set </b><font color="Maroon">f</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">b</font>;<br/>
<b>set </b><font color="Maroon">g</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c</font></span><a href="tarski.html#K1">}</a></span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">d</font>;<br/>
<b>set </b><font color="Maroon">h</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">y</font>;<br/>
<b>set </b><font color="Maroon">k</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">w</font></span><a href="tarski.html#K1">}</a></span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">z</font>;<br/>
<b>set </b><font color="Maroon">m</font> = <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>;<br/>
<b>set </b><font color="Maroon">n</font> = <font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">y</font>,<font color="Maroon">z</font>;<br/>
<a NAME="E3:20"/><i><font color="Green">E40</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">b</font>,<font color="Maroon">d</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="tarski.html#K2">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">w</font></span><a href="tarski.html#K2">}</a></span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T65">FUNCT_4:65</a></i>;<br/>
<a NAME="E4:20"/>
( not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">w</font></span><a href="tarski.html#K2">}</a></span> &amp; not <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">w</font></span><a href="tarski.html#K2">}</a></span> )
 
<b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E5:20"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="tarski.html#K2">}</a></span> <a href="subset_1.html#R1">misses</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">w</font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T57">ZFMISC_1:57</a></i>;<br/>
<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="quaterni.html#K2" target="_self">--&gt;</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">b</font>,<font color="Maroon">d</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="funct_4.html#T32">FUNCT_4:32</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T71">FUNCT_4:71</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">w</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i>, <a class="ref" href="funct_4.html#T71">FUNCT_4:71</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">w</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T45">ENUMSET1:45</a></i>
;<br/>
<b>hence </b><a NAME="E7:20"/>
<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="quaterni.html#K2" target="_self">--&gt;</a> <font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">d</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">w</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
 ;<br/>


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