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

<b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">G</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1">PARTITIONS</a> <font color="Maroon">Y</font></span>)</span>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">D</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">E</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">J</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/>

















<b>assume </b><a NAME="E1:1"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K5">}</a></span> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font> &amp; <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">D</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> )
 ;<br/>

<a NAME="E2:1"/><i><font color="Green">E29</font></i>: 
 <a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">A</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="bvfunc_2.html#D7">BVFUNC_2:def 7</a></i>;<br/>
<a NAME="E3:1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K4">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i>, <a class="ref" href="enumset1.html#T56">ENUMSET1:56</a></i>;<br/>
<a NAME="E4:1"/><i><font color="Green">E31</font></i>: 
not <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:1"/><i><font color="Green">E32</font></i>: 
not <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:1"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:1"/><i><font color="Green">E34</font></i>: 
not <font color="Maroon">E</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E8:1"/><i><font color="Green">E35</font></i>: 
not <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E9:1"/><i><font color="Green">E36</font></i>: 
not <font color="Maroon">J</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E10:1"/><i><font color="Green">E37</font></i>: 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font></span><a href="tarski.html#K2">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font></span><a href="tarski.html#K2">}</a></span>
 
<b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T72">ZFMISC_1:72</a></i>;<br/>
<span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K4">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K3">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T51">ENUMSET1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K3">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T42">XBOOLE_1:42</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K3">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T67">ZFMISC_1:67</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K2">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="enumset1.html#T47">ENUMSET1:47</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K2">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T42">XBOOLE_1:42</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p4"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="tarski.html#K2">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="enumset1.html#T45">ENUMSET1:45</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font></span><a href="tarski.html#K2">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="tarski.html#K2">}</a></span> <a href="subset_1.html#K6">\</a> <span class="p4"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T42">XBOOLE_1:42</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="tarski.html#K2">}</a></span></span>)</span></span>)</span>
<b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T72">ZFMISC_1:72</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="tarski.html#K2">}</a></span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T67">ZFMISC_1:67</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K2">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="enumset1.html#T45">ENUMSET1:45</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">B</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K3">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T47">ENUMSET1:47</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T51">ENUMSET1:51</a></i>
;<br/>
<b>then </b><i><font color="Green">E38</font></i>: <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K4">}</a></span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T42">XBOOLE_1:42</a></i>
<br/>.= 
<a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T37">XBOOLE_1:37</a></i>
;<br/>
<a NAME="E13:1"/><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a>  <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_3"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">J</font>
 ;<br/>

<a NAME="E2:1_3"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">J</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E3:1_3"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">J</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">bcdef</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">j</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:1_3"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">bcdef</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">bcdef</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E6:1_3"/>
<font color="Maroon">bcdef</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span>,<font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E7:1_3"/><b>then </b>
( <font color="Maroon">bcdef</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span>,<font color="Maroon">F</font> &amp; not <font color="Maroon">bcdef</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">bcde</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">f</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E9:1_3"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">bcde</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">bcdef</font> <a href="hidden.html#R1">=</a> <font color="Maroon">bcde</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E10:1_3"/>
<font color="Maroon">bcde</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">E</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E11:1_3"/><b>then </b>
( <font color="Maroon">bcde</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">E</font> &amp; not <font color="Maroon">bcde</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">bcd</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">e</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E13:1_3"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">bcd</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font> &amp; <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font> &amp; <font color="Maroon">bcde</font> <a href="hidden.html#R1">=</a> <font color="Maroon">bcd</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E14:1_3"/>
<font color="Maroon">bcd</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">D</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E15:1_3"/><b>then </b>
( <font color="Maroon">bcd</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">D</font> &amp; not <font color="Maroon">bcd</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">bc</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">d</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E17:1_3"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">bc</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">bcd</font> <a href="hidden.html#R1">=</a> <font color="Maroon">bc</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E18:1_3"/>
<font color="Maroon">bc</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E19:1_3"/><b>then </b>
( <font color="Maroon">bc</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">B</font>,<font color="Maroon">C</font> &amp; not <font color="Maroon">bc</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">b</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">c</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E21:1_3"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">bc</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<b>set </b><font color="Maroon">h</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span>;<br/>
<i><font color="Green">E57</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
<span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">J</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font></span><a href="enumset1.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="bvfunc14.html#T41">BVFUNC14:41</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">J</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font></span><a href="enumset1.html#K3">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T51">ENUMSET1:51</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T55">ENUMSET1:55</a></i>
;<br/>
<i><font color="Green">E58</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
<span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">J</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font></span><a href="enumset1.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="bvfunc14.html#T41">BVFUNC14:41</a></i>
<br/>.= 
<span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">J</font></span><a href="bvfunc_2.html#K4">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font></span><a href="enumset1.html#K3">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T51">ENUMSET1:51</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">E</font>,<font color="Maroon">F</font>,<font color="Maroon">J</font></span><a href="enumset1.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T55">ENUMSET1:55</a></i>
;<br/>
<a NAME="E24:1_3"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="bvfunc14.html#T40">BVFUNC14:40</a></i>;<br/>
<a NAME="E25:1_3"/><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="bvfunc14.html#T40">BVFUNC14:40</a></i>;<br/>
<a NAME="E26:1_3"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="bvfunc14.html#T40">BVFUNC14:40</a></i>;<br/>
<a NAME="E27:1_3"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 
<b>by </b><i>, <a class="ref" href="bvfunc14.html#T40">BVFUNC14:40</a></i>;<br/>
<a NAME="E28:1_3"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="bvfunc14.html#T40">BVFUNC14:40</a></i>;<br/>
<a NAME="E29:1_3"/><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 
<b>by </b><i>, <a class="ref" href="bvfunc14.html#T40">BVFUNC14:40</a></i>;<br/>
<a NAME="E30:1_3"/><i><font color="Green">E65</font></i>: 
for <font color="Olive">p</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">p</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3_3"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:1_3_3"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span>
 ;<br/>

<a NAME="E2:1_3_3"/><b>then </b>
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">J</font> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:1_3_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">p</font>
 <b>by </b><i>, , , , , , <a class="ref" href="bvfunc14.html#T40">BVFUNC14:40</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E31:1_3"/>
<font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E32:1_3"/><b>then </b><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E33:1_3"/>
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E34:1_3"/><b>then </b><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E35:1_3"/>
<font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E36:1_3"/><b>then </b><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E37:1_3"/>
<font color="Maroon">E</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E38:1_3"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E39:1_3"/>
<font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E40:1_3"/><b>then </b><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E41:1_3"/>
<font color="Maroon">J</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E42:1_3"/><b>then </b><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E43:1_3"/><i><font color="Green">E73</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span></span><a href="enumset1.html#K4">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_3_4"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:1_3_4"/><i><font color="Green">E75</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:1_3_4"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">J</font> )
 
<b>by </b><i>, <a class="txt" href="bvfunc24.html#E9:1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:1_3_4"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span></span><a href="enumset1.html#K4">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc24.html#E9:1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E44:1_3"/>
<span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span></span><a href="enumset1.html#K4">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_3_5"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span></span><a href="enumset1.html#K4">}</a></span>
 ;<br/>

<b>hence </b><a NAME="E2:1_3_5"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc24.html#E2:1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="bvfunc24.html#E3:1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="bvfunc24.html#E5:1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="bvfunc24.html#E6:1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="bvfunc24.html#E7:1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E45:1_3"/><b>then </b><i><font color="Green">E76</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span></span><a href="enumset1.html#K4">}</a></span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E8:1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E46:1_3"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_3_6"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:1_3_6"/><b>then </b>
( <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> or <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> or <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> or <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> or <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> or <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> )
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E8:1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:1_3_6"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Y</font>
 <b>by </b><i>, , , , , , , , , , <a class="ref" href="bvfunc24.html#T1" target="_self">Th1</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">FF</font> =  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span></span>)</span> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">Y</font> ;<br/>
<b>reconsider </b><font color="Maroon">h</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">b</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">d</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">j</font></span>)</span> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E49:1_3"/><i><font color="Green">E78</font></i>: 
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">FF</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E2:1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>
<a NAME="E50:1_3"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">FF</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_3_7"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:1_3_7"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">FF</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E9:1"><i><font color="Green">E36</font></i></a></i>;<br/>
<a NAME="E3:1_3_7"/>
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FF</font> holds <br/><font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Olive">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3_7_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:1_3_7_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FF</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3_7_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_3_7_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:1_3_7_1_1_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> )
 </span><b>by </b><i><a class="txt" href="bvfunc24.html#E8:1"><i><font color="Green">E35</font></i></a>, , <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_3_7_1_1_1_1"><b>case </b></a><a NAME="E1:1_3_7_1_1_1_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font>
 ;<br/><div class="add"><a NAME="E2:1_3_7_1_1_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , , , <a class="txt" href="bvfunc24.html#E13:1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E3:1_3_7_1_1_1_1"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E4:1_3_7_1_1_1_1"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E5:1_3_7_1_1_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_3_7_1_1_1_2"><b>case </b></a><a NAME="E1:1_3_7_1_1_1_2"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font>
 ;<br/><div class="add"><a NAME="E2:1_3_7_1_1_1_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , , , <a class="txt" href="bvfunc24.html#E13:1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E3:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E4:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E5:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E6:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E7:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E8:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E9:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E10:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E11:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E12:1_3_7_1_1_1_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E13:1_3_7_1_1_1_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_3_7_1_1_1_3"><b>case </b></a><a NAME="E1:1_3_7_1_1_1_3"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font>
 ;<br/><div class="add"><a NAME="E2:1_3_7_1_1_1_3"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , , , <a class="txt" href="bvfunc24.html#E13:1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E3:1_3_7_1_1_1_3"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E4:1_3_7_1_1_1_3"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E5:1_3_7_1_1_1_3"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E6:1_3_7_1_1_1_3"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">d</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E7:1_3_7_1_1_1_3"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_3_7_1_1_1_4"><b>case </b></a><a NAME="E1:1_3_7_1_1_1_4"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font>
 ;<br/><div class="add"><a NAME="E2:1_3_7_1_1_1_4"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , , , <a class="txt" href="bvfunc24.html#E13:1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E3:1_3_7_1_1_1_4"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E4:1_3_7_1_1_1_4"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><a NAME="E5:1_3_7_1_1_1_4"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E6:1_3_7_1_1_1_4"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_3_7_1_1_1_5"><b>case </b></a><a NAME="E1:1_3_7_1_1_1_5"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font>
 ;<br/><div class="add"><a NAME="E2:1_3_7_1_1_1_5"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">j</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font>
 <b>by </b><i>, , , , , <a class="txt" href="bvfunc24.html#E13:1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><a NAME="E3:1_3_7_1_1_1_5"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_3_7_1_1_1_6"><b>case </b></a><a NAME="E1:1_3_7_1_1_1_6"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:1_3_7_1_1_1_6"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="bvfunc24.html#T1" target="_self">Th1</a>, <a class="txt" href="bvfunc24.html#E13:1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:1_3_7_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:1_3_7"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">FF</font>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E1:1_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:1_3_7"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">FF</font>
 <b>by </b><i><a class="txt" href="bvfunc24.html#E1:1_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E51:1_3"/>
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">FF</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_3_8"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">FF</font>
 ;<br/>

<a NAME="E2:1_3_8"/>
( <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> )
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E9:1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E3:1_3_8"/><b>then </b><i><font color="Green">E91</font></i>: 
( <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">d</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">e</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">j</font> )
 
<b>by </b><i>, , , , , <a class="ref" href="bvfunc24.html#T1" target="_self">Th1</a>, <a class="txt" href="bvfunc24.html#E10:1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="bvfunc24.html#E13:1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E4:1_3_8"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:1_3_8"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E1:1_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:1_3_8"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E1:1_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:1_3_8"/><b>then </b>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">d</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">e</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E1:1_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:1_3_8"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 <b>by </b><i>, , , , , <a class="txt" href="bvfunc24.html#E1:1_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E52:1_3"/><b>then </b><i><font color="Green">E92</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">FF</font>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E12:1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E53:1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E54:1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
 <b>by </b><i>, , <a class="txt" href="bvfunc24.html#E1:1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="bvfunc24.html#E13:1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="bvfunc_2.html#D1">BVFUNC_2:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E14:1"/>
 <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">J</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_2.html#K2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">h</font> being   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">FF</font> being   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E3:1_4"/><i><font color="Green">E93</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">FF</font> &amp; ( for <font color="Olive">d</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> holds <br/><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Olive">d</font> ) &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">FF</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="ref" href="bvfunc_2.html#D1">BVFUNC_2:def 1</a></i>;<br/>
<a NAME="E4:1_4"/><i><font color="Green">E94</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> &amp; <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> &amp; <font color="Maroon">E</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> &amp; <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> &amp; <font color="Maroon">J</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">A</font></span><a href="bvfunc_2.html#K4">}</a></span> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<a NAME="E5:1_4"/><b>then </b><i><font color="Green">E95</font></i>: 
( <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:1_4"/><i><font color="Green">E96</font></i>: 
( <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> )
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E7:1_4"/><b>then </b><i><font color="Green">E97</font></i>: 
 <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">FF</font> <a href="hidden.html#R1">=</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>
<a NAME="E8:1_4"/><i><font color="Green">E98</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E9:1_4"/><i><font color="Green">E99</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">m</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_4_1"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span>
 ;<br/>

<a NAME="E2:1_4_1"/><b>then </b>
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:1_4_1"/><b>then </b><i><font color="Green">E102</font></i>: 
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E4:1_4_1"/><b>then </b>
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:1_4_1"/><b>then </b>
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:1_4_1"/><b>then </b><i><font color="Green">E103</font></i>: 
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> )
 
<b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:1_4_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span></span><a href="enumset1.html#K4">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_4_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_4_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:1_4_1_1"/><i><font color="Green">E104</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font> &amp; <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:1_4_1_1"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> or <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">J</font> )
 
<b>by </b><i>, , , <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:1_4_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K4">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span></span><a href="enumset1.html#K4">}</a></span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:1_4_1"/><b>then </b>
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">h</font> holds <br/><font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Olive">y</font>
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D4">ENUMSET1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E9:1_4_1"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 <b>by </b><i>, , , <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:1_4"/><i><font color="Green">E105</font></i>: 
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_4_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">m</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_4_2"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:1_4_2"/><b>then </b><i><font color="Green">E106</font></i>: 
( <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> &amp; <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> )
 
<b>by </b><i>, , , <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E3:1_4_2"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E4:1_4_2"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:1_4_2"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:1_4_2"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:1_4_2"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E11:1_4"/><b>then </b><i><font color="Green">E107</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p5">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<b>set </b><font color="Maroon">mbc</font> = <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">mbcd</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">mbcde</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">mbcdef</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span>;<br/>
<a NAME="E12:1_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E13:1_4"/><b>then </b><i><font color="Green">E112</font></i>: 
not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E14:1_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E15:1_4"/><b>then </b><i><font color="Green">E113</font></i>: 
not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E16:1_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E17:1_4"/><b>then </b><i><font color="Green">E114</font></i>: 
not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E18:1_4"/>
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, , , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E19:1_4"/><b>then </b><i><font color="Green">E115</font></i>: 
not <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E20:1_4"/>
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">B</font>,<font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E21:1_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <font color="Maroon">B</font>,<font color="Maroon">C</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E22:1_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E23:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">D</font>
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E24:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">D</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E25:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E26:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">E</font>
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E27:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">E</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E28:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font>
 
<b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E29:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span>,<font color="Maroon">F</font>
 
<b>by </b><i>, <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E30:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span>,<font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E31:1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p4">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>
<a NAME="E32:1_4"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K3">INTERSECTION</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">J</font>
 
<b>by </b><i>, , <a class="ref" href="setfam_1.html#D5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E33:1_4"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3">INTERSECTION</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">J</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E34:1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">J</font>
 <b>by </b><i><a class="ref" href="partit1.html#D4">PARTIT1:def 4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E15:1"/>
 <a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">A</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">D</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">E</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">F</font></span>)</span> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">J</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div>
