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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>











<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E14">A1</font></i>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/>

<a NAME="E2:20"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="bvfunc14.html#T5" target="_self" title="BVFUNC14:th.5">Th5</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">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/>
<b>set </b><font color="Maroon" title="c9">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/>
<b>set </b><font color="Maroon" title="c10">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="E3:20"/><i><font color="Green" title="E16">A3</font></i>: 
 <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>
 
<b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="bvfunc14.html#T4" target="_self" title="BVFUNC14:th.4">Th4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c11">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="E4:20"/>
 <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>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E5:20"/><b>then </b><i><font color="Green" title="E17">A4</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E6:20"/><i><font color="Green" title="E18">A5</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E7:20"/><i><font color="Green" title="E19">A6</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E8:20"/><i><font color="Green" title="E20">A7</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>then </b><i><font color="Green" title="E21">A8</font></i>:  <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>
<b>by </b><i><a class="txt" href="#E5:20"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="#E6:20"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E7:20"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>
<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>
<b>by </b><i><a class="ref" href="enumset1.html#T41" title="ENUMSET1:th.41">ENUMSET1:41</a></i>
<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>
<b>by </b><i><a class="ref" href="enumset1.html#T43" title="ENUMSET1:th.43">ENUMSET1:43</a></i>
;<br/>
<a NAME="E10:20"/><i><font color="Green" title="E22">A9</font></i>: 
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>proof </b></a><div class="add">

<a NAME="E1:20_2"/>
<font color="Maroon" 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>
 
<b>by </b><i><a class="txt" href="#E8:20"><i><font color="Green" title="E20">A7</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:20_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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>
 
<b>by </b><i><a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E3:20_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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>
 <b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E11:20"/><i><font color="Green" title="E23">A10</font></i>: 
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_3"><b>proof </b></a><div class="add">

<a NAME="E1:20_3"/>
not <font color="Maroon" 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>
 
<b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E8:20"><i><font color="Green" title="E20">A7</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:20_3"/><b>then </b><i><font color="Green" title="E24">A11</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/>
<a NAME="E3:20_3"/>
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>
 
<b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E7:20"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:20_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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>
 
<b>by </b><i><a class="txt" href="#E2:20_3"><i><font color="Green" title="E24">A11</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/>
<b>hence </b><a NAME="E5:20_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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>
 <b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E12:20"/><i><font color="Green" title="E24">A12</font></i>: 
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_4"><b>proof </b></a><div class="add">

<a NAME="E1:20_4"/>
not <font color="Maroon" 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>
 
<b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E8:20"><i><font color="Green" title="E20">A7</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:20_4"/><b>then </b><i><font color="Green" title="E25">A13</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/>
<a NAME="E3:20_4"/>
<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>
 
<b>by </b><i><a class="txt" href="#E7:20"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:20_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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>
 
<b>by </b><i><a class="txt" href="#E2:20_4"><i><font color="Green" title="E25">A13</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E5:20_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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>
 <b>by </b><i><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E13:20"/><i><font color="Green" title="E25">A14</font></i>: 
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="20_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c12">d</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c12">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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font> )</span><br/>

<b>assume </b><a NAME="E1:20_5"/><i><font color="Green" title="E26">A15</font></i>: 
<font color="Maroon" title="c12">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:()"><i><font color="Red">::  thesis: </font></i></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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_5_1_1"/>
( <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> or <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> or <font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C</font> )
 </span><b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E1:20_5"><i><font color="Green" title="E26">A15</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_5_1_1_1"><b>case </b></a><a NAME="E1:20_5_1_1_1"/>
<font color="Maroon" title="c12">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:()"><i><font color="Red">::  thesis: </font></i></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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font></span><br/><div class="add"><b>hence </b><a NAME="E2:20_5_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font>
 <b>by </b><i><a class="txt" href="#E10:20"><i><font color="Green" title="E22">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_5_1_1_2"><b>case </b></a><a NAME="E1:20_5_1_1_2"/>
<font color="Maroon" title="c12">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:()"><i><font color="Red">::  thesis: </font></i></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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font></span><br/><div class="add"><b>hence </b><a NAME="E2:20_5_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font>
 <b>by </b><i><a class="txt" href="#E11:20"><i><font color="Green" title="E23">A10</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_5_1_1_3"><b>case </b></a><a NAME="E1:20_5_1_1_3"/>
<font color="Maroon" title="c12">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:()"><i><font color="Red">::  thesis: </font></i></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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font></span><br/><div class="add"><b>hence </b><a NAME="E2:20_5_1_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font>
 <b>by </b><i><a class="txt" href="#E12:20"><i><font color="Green" title="E24">A12</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" 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="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E14:20"/>
<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>
 
<b>by </b><i><a class="txt" href="#E9:20"><i><font color="Green" title="E21">A8</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E15:20"/><b>then </b><i><font color="Green" title="E26">A16</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E16:20"/>
<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>
 
<b>by </b><i><a class="txt" href="#E9:20"><i><font color="Green" title="E21">A8</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E17:20"/><b>then </b><i><font color="Green" title="E27">A17</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E18:20"/>
<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>
 
<b>by </b><i><a class="txt" href="#E9:20"><i><font color="Green" title="E21">A8</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<a NAME="E19:20"/><b>then </b><i><font color="Green" title="E28">A18</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E20:20"/><i><font color="Green" title="E29">A19</font></i>: 
 <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="20_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c12">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E1:20_6"/>
<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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>then consider </b><font color="Maroon" title="c13">x1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:20_6"/><i><font color="Green" title="E30">A20</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_6_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_6_1_1"/>
( <font color="Maroon" 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><b>by </b><i><a class="txt" href="#E9:20"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="#E3:20_6"><i><font color="Green" title="E30">A20</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_6_1_1_1"><b>case </b></a><a NAME="E1:20_6_1_1_1"/>
<font color="Maroon" 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:()"><i><font color="Red">::  thesis: </font></i></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"><b>hence </b><a NAME="E2:20_6_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>
 <b>by </b><i><a class="txt" href="#E3:20_6"><i><font color="Green" title="E30">A20</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_6_1_1_2"><b>case </b></a><a NAME="E1:20_6_1_1_2"/>
<font color="Maroon" 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:()"><i><font color="Red">::  thesis: </font></i></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"><b>hence </b><a NAME="E2:20_6_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>
 <b>by </b><i><a class="txt" href="#E3:20_6"><i><font color="Green" title="E30">A20</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_6_1_1_3"><b>case </b></a><a NAME="E1:20_6_1_1_3"/>
<font color="Maroon" 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:()"><i><font color="Red">::  thesis: </font></i></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"><b>hence </b><a NAME="E2:20_6_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>
 <b>by </b><i><a class="txt" href="#E3:20_6"><i><font color="Green" title="E30">A20</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20_6"/>
<font color="Maroon" 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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E21:20"/>
 <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="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c12">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font> )</span><br/>

<b>assume </b><a NAME="E1:20_7"/><i><font color="Green" title="E30">A21</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_7_1_1"/>
( <font color="Maroon" 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><b>by </b><i><a class="txt" href="#E20:20"><i><font color="Green" title="E29">A19</font></i></a>, <a class="txt" href="#E1:20_7"><i><font color="Green" title="E30">A21</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_7_1_1_1"><b>case </b></a><a NAME="E1:20_7_1_1_1"/>
<font color="Maroon" 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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font></span><br/><div class="add"><b>hence </b><a NAME="E2:20_7_1_1_1"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="txt" href="#E10:20"><i><font color="Green" title="E22">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_7_1_1_2"><b>case </b></a><a NAME="E1:20_7_1_1_2"/>
<font color="Maroon" 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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font></span><br/><div class="add"><b>hence </b><a NAME="E2:20_7_1_1_2"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="txt" href="#E11:20"><i><font color="Green" title="E23">A10</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_7_1_1_3"><b>case </b></a><a NAME="E1:20_7_1_1_3"/>
<font color="Maroon" 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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font></span><br/><div class="add"><b>hence </b><a NAME="E2:20_7_1_1_3"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font>
 <b>by </b><i><a class="txt" href="#E12:20"><i><font color="Green" title="E24">A12</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_7"/>
<font color="Maroon" title="c12">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><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="E23:20"/><i><font color="Green" title="E30">A22</font></i>: 
 <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>
 
<b>by </b><i><a class="txt" href="#E15:20"><i><font color="Green" title="E26">A16</font></i></a>, <a class="ref" href="setfam_1.html#D10" title="SETFAM_1:def.10">SETFAM_1:def 10</a></i>;<br/>
<a NAME="E24:20"/>
 <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> 
 
<b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E9:20"><i><font color="Green" title="E21">A8</font></i></a>, <a class="txt" href="#E13:20"><i><font color="Green" title="E25">A14</font></i></a>, <a class="ref" href="bvfunc_2.html#D5" title="BVFUNC_2:def.5">BVFUNC_2:def 5</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c13">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E26:20"/><i><font color="Green" title="E31">A23</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E27:20"/><i><font color="Green" title="E32">A24</font></i>: 
( <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> &amp; <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> &amp; <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> )
 
<b>by </b><i><a class="txt" href="#E15:20"><i><font color="Green" title="E26">A16</font></i></a>, <a class="txt" href="#E17:20"><i><font color="Green" title="E27">A17</font></i></a>, <a class="txt" href="#E19:20"><i><font color="Green" title="E28">A18</font></i></a>, <a class="txt" href="#E23:20"><i><font color="Green" title="E30">A22</font></i></a>, <a class="txt" href="#E26:20"><i><font color="Green" title="E31">A23</font></i></a>, <a class="ref" href="setfam_1.html#D1" title="SETFAM_1:def.1">SETFAM_1:def 1</a></i>;<br/>
<a NAME="E28:20"/><i><font color="Green" title="E33">A25</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="bvfunc14.html#T1" target="_self" title="BVFUNC14:th.1">Th1</a></i>;<br/>
<a NAME="E29:20"/>
<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>
 
<b>by </b><i><a class="txt" href="#E11:20"><i><font color="Green" title="E23">A10</font></i></a>, <a class="txt" href="#E12:20"><i><font color="Green" title="E24">A12</font></i></a>, <a class="txt" href="#E27:20"><i><font color="Green" title="E32">A24</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E30:20"/><b>then </b>
<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> 
 
<b>by </b><i><a class="txt" href="#E10:20"><i><font color="Green" title="E22">A9</font></i></a>, <a class="txt" href="#E27:20"><i><font color="Green" title="E32">A24</font></i></a>, <a class="txt" href="#E28:20"><i><font color="Green" title="E33">A25</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c14">p</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E32:20"/><i><font color="Green" title="E34">A26</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><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> <b>by </b><i><a class="txt" href="#E32:20"><i><font color="Green" title="E34">A26</font></i></a></i>;<br/>
<b>set </b><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="E34:20"/><i><font color="Green" title="E35">A27</font></i>: 
( <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;  <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#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font> )
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></i>;<br/>
<a NAME="E35:20"/>
( <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> &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> )
 
<b>by </b><i><a class="txt" href="#E32:20"><i><font color="Green" title="E34">A26</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E36:20"/><b>then </b><i><font color="Green" title="E36">A28</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="#E34:20"><i><font color="Green" title="E35">A27</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E37:20"/><b>then </b><i><font color="Green" title="E37">A29</font></i>: 
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>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E38:20"/>
<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>
 
<b>by </b><i><a class="ref" href="setfam_1.html#D5" title="SETFAM_1:def.5">SETFAM_1:def 5</a></i>;<br/>
<a NAME="E39:20"/><b>then </b>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#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>
 
<b>by </b><i><a class="txt" href="#E37:20"><i><font color="Green" title="E37">A29</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/>
<a NAME="E40:20"/><b>then </b><i><font color="Green" title="E38">A30</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="partit1.html#D4" title="PARTIT1:def.4">PARTIT1:def 4</a></i>;<br/>
<b>set </b><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="E41:20"/><i><font color="Green" title="E39">A31</font></i>: 
 <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>
 
<b>by </b><i><a class="txt" href="#E1:20"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="bvfunc11.html#T3" title="BVFUNC11:th.3">BVFUNC11:3</a></i>;<br/>
<a NAME="E42:20"/><i><font color="Green" title="E40">A32</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="#E32:20"><i><font color="Green" title="E34">A26</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E43:20"/>
<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>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></i>;<br/>
<a NAME="E44:20"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="#E41:20"><i><font color="Green" title="E39">A31</font></i></a>, <a class="txt" href="#E42:20"><i><font color="Green" title="E40">A32</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E45:20"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T50" title="EQREL_1:th.50">EQREL_1:50</a></i>;<br/>
<a NAME="E46:20"/><b>then </b><i><font color="Green" title="E41">A33</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></i>;<br/>
<a NAME="E47:20"/>
<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>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></i>;<br/>
<a NAME="E48:20"/><b>then </b><i><font color="Green" title="E42">A34</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="#E46:20"><i><font color="Green" title="E41">A33</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E49:20"/><i><font color="Green" title="E43">A35</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></i>;<br/>
<a NAME="E50:20"/>
( <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> )
 
<b>by </b><i><a class="txt" href="#E2:20"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="#E40:20"><i><font color="Green" title="E38">A30</font></i></a>, <a class="ref" href="eqrel_1.html#D6" title="EQREL_1:def.6">EQREL_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E51:20"/>
 <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>
 <b>by </b><i><a class="txt" href="#E3:20"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="#E36:20"><i><font color="Green" title="E36">A28</font></i></a>, <a class="txt" href="#E42:20"><i><font color="Green" title="E40">A32</font></i></a>, <a class="txt" href="#E48:20"><i><font color="Green" title="E42">A34</font></i></a>, <a class="txt" href="#E49:20"><i><font color="Green" title="E43">A35</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
