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<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</font></span>)</span><br/> for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font>, <font color="Olive" title="b4">C</font> being   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font><br/> for <font color="Olive" title="b5">z</font>, <font color="Olive" title="b6">u</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>  &amp; <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B</font>,<font color="Olive" title="b4">C</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> &amp; <font color="Olive" title="b2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">C</font> &amp; <font color="Olive" title="b4">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">A</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b5">z</font>,<font color="Olive" title="b4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b6">u</font>,<font color="Olive" title="b4">C</font> holds <br/> <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b6">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">G</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b5">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Olive" title="b3">B</font>,<font color="Olive" title="b1">G</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</font> being   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font><br/> for <font color="Olive" title="b4">z</font>, <font color="Olive" title="b5">u</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Maroon" title="c2">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>  &amp; <font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> &amp; <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b3">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">A</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b4">z</font>,<font color="Olive" title="b3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b5">u</font>,<font color="Olive" title="b3">C</font> holds <br/> <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b5">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Olive" title="b1">A</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b4">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Olive" title="b2">B</font>,<font color="Maroon" title="c2">G</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">z</font>, <font color="Olive" title="b2">u</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Maroon" title="c2">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>  &amp; <font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> &amp; <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c5">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b1">z</font>,<font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b2">u</font>,<font color="Maroon" title="c5">C</font> holds <br/> <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b2">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Olive" title="b1">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">z</font>, <font color="Maroon" title="c7">u</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>  &amp; <font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> &amp; <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">B</font> &amp; <font color="Maroon" title="c4">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c5">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font> implies  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font></span>)</span> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:23"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c2">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a> 
 <span class="kw">and </span><br/><a NAME="E2:23"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E3:23"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">B</font>
 <span class="kw">and </span><br/><a NAME="E4:23"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c4">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">C</font>
 <span class="kw">and </span><br/><a NAME="E5:23"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
<font color="Maroon" title="c5">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E6:23"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">h</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span>;<br/>
<a NAME="E7:23"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c3">A</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E8:23"/><span class="kw">then </span>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E9:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>;<br/>
<a NAME="E10:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">H</font> =  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">I</font> =  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">GG</font> =  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font></span>)</span>;<br/>
<a NAME="E11:23"/><span class="lab"><font color="Green" title="E21">A9</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc14.html#T1" target="_self" title="BVFUNC14:th.1">Th1</a></span>;<br/>
<a NAME="E12:23"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E13:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A10</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E14:23"/><span class="lab"><font color="Green" title="E23">A11</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">C</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E15:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A12</font></span>: 
<font color="Maroon" title="c5">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E16:23"/>
not <font color="Maroon" title="c4">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E17:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A13</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>;<br/>
<a NAME="E18:23"/>
not <font color="Maroon" title="c4">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E14:23"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E19:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>;<br/>
<a NAME="E20:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A14</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>;<br/>
<a NAME="E21:23"/>
not <font color="Maroon" title="c5">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E22:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>;<br/>
<a NAME="E23:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>;<br/>
<a NAME="E24:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A15</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>;<br/>
<a NAME="E25:23"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E28">A16</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c3">A</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">C</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E14:23"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">C</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T41" title="ENUMSET1:th.41">ENUMSET1:41</a></span>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c5">C</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T43" title="ENUMSET1:th.43">ENUMSET1:43</a></span>
;<br/>
<a NAME="E27:23"/><span class="lab"><font color="Green" title="E29">A17</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c12">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> or <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:23_2"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:23_2"/><span class="lab"><font color="Green" title="E30">A18</font></span>: 
<font color="Maroon" title="c13">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:23_2"/><span class="lab"><font color="Green" title="E31">A19</font></span>: 
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">x1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:23_2_1_1"/>
( <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> or <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> or <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:23"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E3:23_2"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:23_2_1_1_1"/>
<font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_2_1_1_1"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23_2"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:23_2_1_1_2"/>
<font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_2_1_1_2"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23_2"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1_3"><span class="kw">case </span></a><a NAME="E1:23_2_1_1_3"/>
<font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_2_1_1_3"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23_2"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:23_2"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p0">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font></span>)</span></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E28:23"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c12">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> or <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:23_3"/><span class="lab"><font color="Green" title="E30">A20</font></span>: 
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_3_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:23_3_1_1"/>
( <font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">A</font> or <font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font> or <font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:23"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E1:23_3"><span class="lab"><font color="Green" title="E30">A20</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1_1"><span class="kw">case </span></a><a NAME="E1:23_3_1_1_1"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_3_1_1_1"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E20">A8</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1_2"><span class="kw">case </span></a><a NAME="E1:23_3_1_1_2"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_3_1_1_2"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:23"><span class="lab"><font color="Green" title="E26">A14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1_3"><span class="kw">case </span></a><a NAME="E1:23_3_1_1_3"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_3_1_1_3"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:23"><span class="lab"><font color="Green" title="E27">A15</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:23_3"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">FF</font> =  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Y</font> ;<br/>
<a NAME="E30:23"/><span class="lab"><font color="Green" title="E30">A21</font></span>: 
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></span>;<br/>
<a NAME="E31:23"/>
for <font color="Olive" title="b1">d</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">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" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c13">d</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:23_4"/><span class="lab"><font color="Green" title="E31">A22</font></span>: 
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_4_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_4_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:23_4_1_1"/>
( <font color="Maroon" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> or <font color="Maroon" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> or <font color="Maroon" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E1:23_4"><span class="lab"><font color="Green" title="E31">A22</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_4_1_1_1"><span class="kw">case </span></a><a NAME="E1:23_4_1_1_1"/>
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_4_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E20">A8</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_4_1_1_2"><span class="kw">case </span></a><a NAME="E1:23_4_1_1_2"/>
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_4_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:23"><span class="lab"><font color="Green" title="E26">A14</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_4_1_1_3"><span class="kw">case </span></a><a NAME="E1:23_4_1_1_3"/>
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:23_4_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:23"><span class="lab"><font color="Green" title="E27">A15</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:23_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E32:23"/><span class="kw">then </span>
 <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c12">FF</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E26:23"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="ref" href="bvfunc_2.html#D5" title="BVFUNC_2:def.5">BVFUNC_2:def 5</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E34:23"/><span class="lab"><font color="Green" title="E31">A23</font></span>: 
<font color="Maroon" title="c13">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c12">FF</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/>
<a NAME="E35:23"/>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:23"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E36:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A24</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E37:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A25</font></span>: 
 <a href="setfam_1.html#K8" title="SETFAM_1:func.8">Intersect</a> <font color="Maroon" title="c12">FF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p5">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D10" title="SETFAM_1:def.10">SETFAM_1:def 10</a></span>;<br/>
<a NAME="E38:23"/>
<font color="Maroon" title="c5">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:23"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E39:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E40:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A26</font></span>: 
<font color="Maroon" title="c13">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:23"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E34:23"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>;<br/>
<a NAME="E41:23"/>
<font color="Maroon" title="c4">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:23"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></span>;<br/>
<a NAME="E42:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/>
<a NAME="E43:23"/><span class="kw">then </span>
<font color="Maroon" title="c13">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:23"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E34:23"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>;<br/>
<a NAME="E44:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A27</font></span>: 
<font color="Maroon" title="c13">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:23"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="txt" href="#E24:23"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E40:23"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E45:23"/>
<font color="Maroon" title="c13">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">C</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<font color="Maroon" title="c5">C</font></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:23"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E37:23"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E34:23"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></span>;<br/>
<a NAME="E46:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E11:23"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E44:23"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">p</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E48:23"/><span class="lab"><font color="Green" title="E36">A28</font></span>: 
<font color="Maroon" title="c14">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">p</font> = <font color="Maroon" title="c14">p</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:23"><span class="lab"><font color="Green" title="E36">A28</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">K</font> =  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font>;<br/>
<a NAME="E50:23"/><span class="lab"><font color="Green" title="E37">A29</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="setfam_1.html#K3" title="SETFAM_1:func.3">INTERSECTION</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D5" title="SETFAM_1:def.5">SETFAM_1:def 5</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">L</font> =  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">C</font>;<br/>
<a NAME="E51:23"/><span class="lab"><font color="Green" title="E38">A30</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></span>;<br/>
<a NAME="E52:23"/><span class="lab"><font color="Green" title="E39">A31</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:23"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E53:23"/>
( <font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:23"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E54:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A32</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E55:23"/><span class="kw">then </span>
not <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E56:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K3" title="SETFAM_1:func.3">INTERSECTION</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c5">C</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:23"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E57:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A33</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partit1.html#D4" title="PARTIT1:def.4">PARTIT1:def 4</a></span>;<br/>
<a NAME="E58:23"/>
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:23"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="bvfunc11.html#T3" title="BVFUNC11:th.3">BVFUNC11:3</a></span>;<br/>
<a NAME="E59:23"/><span class="kw">then </span>
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:23"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="txt" href="#E51:23"><span class="lab"><font color="Green" title="E38">A30</font></span></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>;<br/>
<a NAME="E60:23"/><span class="kw">then </span>
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T50" title="EQREL_1:th.50">EQREL_1:50</a></span>;<br/>
<a NAME="E61:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A34</font></span>: 
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></span>;<br/>
<a NAME="E62:23"/>
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></span>;<br/>
<a NAME="E63:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A35</font></span>: 
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:23"><span class="lab"><font color="Green" title="E42">A34</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E64:23"/>
 <a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="bvfunc14.html#T5" target="_self" title="BVFUNC14:th.5">Th5</a></span>;<br/>
<a NAME="E65:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A36</font></span>: 
( <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font></span>)</span> or <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c5">C</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:23"><span class="lab"><font color="Green" title="E41">A33</font></span></a>, <a class="ref" href="eqrel_1.html#D6" title="EQREL_1:def.6">EQREL_1:def 6</a></span>;<br/>
<a NAME="E66:23"/>
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="partit1.html#K2" title="PARTIT1:func.2">'/\'</a> <font color="Maroon" title="c5">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="bvfunc14.html#T4" target="_self" title="BVFUNC14:th.4">Th4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E67:23"/>
 <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c7">u</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c6">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:23"><span class="lab"><font color="Green" title="E40">A32</font></span></a>, <a class="txt" href="#E52:23"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="txt" href="#E63:23"><span class="lab"><font color="Green" title="E43">A35</font></span></a>, <a class="txt" href="#E30:23"><span class="lab"><font color="Green" title="E30">A21</font></span></a>, <a class="txt" href="#E65:23"><span class="lab"><font color="Green" title="E44">A36</font></span></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
