<?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">z</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>, <font color="Maroon">u</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>;<br/>











<b>assume </b><a NAME="E1:20"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">G</font> is <a href="bvfunc_2.html#V2">independent</a> &amp; <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="enumset1.html#K1">}</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">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">A</font> &amp;  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font> )
 ;<br/>

<a NAME="E2:20"/><b>then </b><i><font color="Green">E22</font></i>: 
 <a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">B</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font>
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">H</font> =  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">B</font>,<font color="Maroon">G</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">I</font> =  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font>;<br/>
<b>set </b><font color="Maroon">GG</font> =  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span>;<br/>
<a NAME="E3:20"/><i><font color="Green">E23</font></i>: 
 <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<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="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">A</font>,<font color="Maroon">G</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>set </b><font color="Maroon">h</font> = <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> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span>;<br/>
<a NAME="E4:20"/>
 <a href="relat_1.html#K1">dom</a> <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> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E5:20"/><b>then </b><i><font color="Green">E24</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E6:20"/><i><font color="Green">E25</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <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>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E7:20"/><i><font color="Green">E26</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E8:20"/><i><font color="Green">E27</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</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="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<b>then </b><i><font color="Green">E28</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</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#K4">\/</a> <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></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="bvfunc14.html#T1" target="_self">Th1</a>, , , <a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4">{</a><span class="default"><font color="Maroon">C</font></span><a href="bvfunc_2.html#K4">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>
;<br/>
<a NAME="E10:20"/><i><font color="Green">E29</font></i>: 
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:20_2"/><b>then </b>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E3:20_2"/>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E11:20"/><i><font color="Green">E30</font></i>: 
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_3"><b>proof </b></a><div class="add">

<a NAME="E1:20_3"/>
not <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"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:20_3"/><b>then </b><i><font color="Green">E31</font></i>: 
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <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> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E3:20_3"/>
not <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"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:20_3"/><b>then </b>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E3:20"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<b>hence </b><a NAME="E5:20_3"/>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:20"/><i><font color="Green">E32</font></i>: 
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_4"><b>proof </b></a><div class="add">

<a NAME="E1:20_4"/>
not <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"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:20_4"/><b>then </b><i><font color="Green">E35</font></i>: 
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <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> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<a NAME="E3:20_4"/>
<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"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:20_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">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E5:20"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E5:20_4"/>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E13:20"/><i><font color="Green">E36</font></i>: 
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> holds <br/><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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Olive">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_5"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:20_5"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_5_1_1"/>
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> or <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> or <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> )
 </span><b>by </b><i>, <a class="txt" href="bvfunc14.html#E6:20"><i><font color="Green">E25</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_5_1_1_1"><b>case </b></a><a NAME="E1:20_5_1_1_1"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_5_1_1_1"/>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">d</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_5_1_1_2"><b>case </b></a><a NAME="E1:20_5_1_1_2"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_5_1_1_2"/>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E2:20"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_5_1_1_3"><b>case </b></a><a NAME="E1:20_5_1_1_3"/>
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_5_1_1_3"/>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E3:20"><i><font color="Green">E23</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_5"/>
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">d</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E14:20"/>
<font color="Maroon">A</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E15:20"/><b>then </b><i><font color="Green">E38</font></i>: 
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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="E16:20"/>
<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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E17:20"/><b>then </b><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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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="E18:20"/>
<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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E19:20"/><b>then </b><i><font color="Green">E47</font></i>: 
<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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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="E20:20"/><i><font color="Green">E48</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span><a href="enumset1.html#K1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_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="E1:20_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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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="E3:20_6"/><i><font color="Green">E49</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_6_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_6_1_1"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> or <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> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="bvfunc14.html#E10:20"><i><font color="Green">E29</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_6_1_1_1"><b>case </b></a><a NAME="E1:20_6_1_1_1"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_6_1_1_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E10:20"><i><font color="Green">E29</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_6_1_1_2"><b>case </b></a><a NAME="E1:20_6_1_1_2"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_6_1_1_2"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E10:20"><i><font color="Green">E29</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_6_1_1_3"><b>case </b></a><a NAME="E1:20_6_1_1_3"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_6_1_1_3"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="bvfunc14.html#E10:20"><i><font color="Green">E29</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_6"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></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> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font></span>)</span></span><a href="enumset1.html#K1">}</a></span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E21:20"/>
 <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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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="20_7"><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="E1:20_7"/><i><font color="Green">E50</font></i>: 
<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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_7_1_1"/>
( <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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> )
 </span><b>by </b><i><a class="txt" href="bvfunc14.html#E9:20"><i><font color="Green">E28</font></i></a>, <a class="txt" href="bvfunc14.html#E10:20"><i><font color="Green">E29</font></i></a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_7_1_1_1"><b>case </b></a><a NAME="E1:20_7_1_1_1"/>
<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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_7_1_1_1"/>
<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/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_7_1_1_2"><b>case </b></a><a NAME="E1:20_7_1_1_2"/>
<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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_7_1_1_2"/>
<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="txt" href="bvfunc14.html#E2:20"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_7_1_1_3"><b>case </b></a><a NAME="E1:20_7_1_1_3"/>
<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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_7_1_1_3"/>
<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="txt" href="bvfunc14.html#E3:20"><i><font color="Green">E23</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_7"/>
<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>
 ;<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"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">Y</font> ;<br/>
<a NAME="E23:20"/><i><font color="Green">E52</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> <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="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E6:20"><i><font color="Green">E25</font></i></a>, <a class="ref" href="setfam_1.html#D10">SETFAM_1:def 10</a></i>;<br/>
<a NAME="E24:20"/>
 <a href="setfam_1.html#K8">Intersect</a> <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="bvfunc14.html#E1:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="bvfunc14.html#E5:20"><i><font color="Green">E24</font></i></a>, <a class="ref" href="bvfunc_2.html#D5">BVFUNC_2:def 5</a></i>;<br/>
<b>then consider </b><font color="Maroon">m</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E26:20"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">m</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="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E27:20"/><i><font color="Green">E55</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">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> &amp; <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">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <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> <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="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> )
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E6:20"><i><font color="Green">E25</font></i></a>, <a class="txt" href="bvfunc14.html#E7:20"><i><font color="Green">E26</font></i></a>, <a class="txt" href="bvfunc14.html#E8:20"><i><font color="Green">E27</font></i></a>, <a class="txt" href="bvfunc14.html#E10:20"><i><font color="Green">E29</font></i></a>, <a class="txt" href="bvfunc14.html#E11:20"><i><font color="Green">E30</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E28:20"/><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E29:20"/>
<font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<font color="Maroon">C</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E2:20"><i><font color="Green">E22</font></i></a>, <a class="txt" href="bvfunc14.html#E3:20"><i><font color="Green">E23</font></i></a>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E30:20"/><b>then </b>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</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="txt" href="bvfunc14.html#E12:20"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">p</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E32:20"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">p</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">K</font> =  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font>;<br/>
<a NAME="E34:20"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font> &amp;  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E35:20"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</a> <font color="Maroon">C</font></span>)</span> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E36:20"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<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="E37:20"/><b>then </b><i><font color="Green">E68</font></i>: 
not <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<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="E38:20"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<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">A</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="E39:20"/><b>then </b>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<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">A</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="txt" href="bvfunc14.html#E13:20"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E40:20"/><b>then </b><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">A</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/>
<b>set </b><font color="Maroon">L</font> =  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">C</font>;<br/>
<a NAME="E41:20"/><i><font color="Green">E70</font></i>: 
 <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<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="tarski.html#R1">c=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="bvfunc11.html#T3">BVFUNC11:3</a></i>;<br/>
<a NAME="E42:20"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="partit1.html#K2">'/\'</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="E43:20"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E44:20"/><b>then </b>
 <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">C</font>
 
<b>by </b><i><a class="txt" href="bvfunc14.html#E15:20"><i><font color="Green">E38</font></i></a>, <a class="txt" href="bvfunc14.html#E17:20"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E45:20"/><b>then </b>
 <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#T9">T_1TOPSP:9</a></i>;<br/>
<a NAME="E46:20"/><b>then </b><i><font color="Green">E72</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E47:20"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E48:20"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<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="E49:20"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">B</font>,<font color="Maroon">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="t_1topsp.html#D1">T_1TOPSP:def 1</a></i>;<br/>
<a NAME="E50:20"/>
( <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">B</font>,<font color="Maroon">G</font></span>)</span> or <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">p</font>,<font color="Maroon">C</font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">B</font>,<font color="Maroon">G</font></span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="eqrel_1.html#D6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E51:20"/>
 <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">A</font>,<font color="Maroon">G</font></span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">B</font>,<font color="Maroon">G</font></span>)</span>
 <b>by </b><i>, , <a class="txt" href="bvfunc14.html#E17:20"><i><font color="Green">E39</font></i></a>, , , <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


</div>
