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<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>)<br/>  for <font color="Olive" title="b2">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="b3">P</font>, <font color="Olive" title="b4">Q</font> being    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b2">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>  holds <br/> <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">G</font>)</span>)</span>,<font color="Olive" title="b4">Q</font>,<font color="Olive" title="b2">G</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">Q</font>,<font color="Olive" title="b2">G</font>)</span>)</span>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">G</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</font></span>)</span><br/>  for <font color="Olive" title="b2">P</font>, <font color="Olive" title="b3">Q</font> being    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</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>  holds <br/> <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b2">P</font>,<font color="Olive" title="b1">G</font>)</span>)</span>,<font color="Olive" title="b3">Q</font>,<font color="Olive" title="b1">G</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b3">Q</font>,<font color="Olive" title="b1">G</font>)</span>)</span>,<font color="Olive" title="b2">P</font>,<font color="Olive" title="b1">G</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">G</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1" title="BVFUNC_2:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q</font> being    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Maroon" title="c3">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>  holds <br/> <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<font color="Olive" title="b2">Q</font>,<font color="Maroon" title="c3">G</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b2">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<font color="Olive" title="b1">P</font>,<font color="Maroon" title="c3">G</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">P</font>, <font color="Maroon" title="c5">Q</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a>  implies  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>) )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">A</font> = <font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">B</font> = <font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span>;<br/>
<a NAME="E1:16"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 <a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_2.html#D7" title="BVFUNC_2:def.7">BVFUNC_2:def 7</a></span>;<br/>
<a NAME="E2:16"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
( <font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">G</font> &amp; <font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">G</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></span>;<br/>
<a NAME="E3:16"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
 <a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_2.html#D7" title="BVFUNC_2:def.7">BVFUNC_2:def 7</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:16"/>
<font color="Maroon" title="c3">G</font> is  <a href="bvfunc_2.html#V2" title="BVFUNC_2:attr.2">independent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span><br/>

<a NAME="E5:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="partit_2.html#T14" target="_self" title="PARTIT_2:th.14">Th16</a></span>;<br/>
<a NAME="E6:16"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
 for <font color="Olive" title="b1">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> holds <br/> ( ( (  for <font color="Olive" title="b2">x</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="b2">x</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="Olive" title="b1">y</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) holds <br/><span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) implies <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) &amp; (  ex <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b2">x</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="Olive" title="b1">y</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) &amp;  not <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) implies <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( (  for <font color="Olive" title="b1">x</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">x</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="c8">y</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) holds <br/><span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) implies <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) &amp; (  ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</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="c8">y</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) &amp;  not <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) implies <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  ) )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</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="c8">y</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) &amp;  not <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) implies <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:16_1_1"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
 for <font color="Olive" title="b1">x</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">x</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="c8">y</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) holds <br/><span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/><a NAME="E2:16_1_1"/>
 for <font color="Olive" title="b1">x</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">x</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="c8">y</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">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) holds <br/><span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">x</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="c8">y</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">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) implies <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:16_1_1_1"/>
<font color="Maroon" title="c9">x</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="c8">y</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">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/>

<a NAME="E2:16_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c8">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="partit_2.html#T5" target="_self" title="PARTIT_2:th.5">Th5</a></span>;<br/>
<a NAME="E3:16_1_1_1"/>
 for <font color="Olive" title="b1">z</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">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="c9">x</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) holds <br/><font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">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="c9">x</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>) implies <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:16_1_1_1_1"/>
<font color="Maroon" title="c10">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="c9">x</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/>

<a NAME="E2:16_1_1_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">z</font>,<font color="Maroon" title="c9">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="partit_2.html#T5" target="_self" title="PARTIT_2:th.5">Th5</a></span>;<br/>
<a NAME="E3:16_1_1_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">z</font>,<font color="Maroon" title="c8">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E2:16_1_1_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="relat_1.html#D8" title="RELAT_1:def.8">RELAT_1:def 8</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E5:16_1_1_1_1"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">z</font>,<font color="Maroon" title="c11">u</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:16_1_1_1_1"/><span class="lab"><font color="Green" title="E21">A9</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c8">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D8" title="RELAT_1:def.8">RELAT_1:def 8</a></span>;<br/>
<a NAME="E7:16_1_1_1_1"/>
<font color="Maroon" title="c11">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16_1_1_1_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="relat_1.html#T15" title="RELAT_1:th.15">RELAT_1:15</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">u</font> = <font color="Maroon" title="c11">u</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_1.html#T12" title="ORDERS_1:th.12">ORDERS_1:12</a></span>;<br/>
<a NAME="E9:16_1_1_1_1"/>
<font color="Maroon" title="c12">u</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="c8">y</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E6:16_1_1_1_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="partit_2.html#T5" target="_self" title="PARTIT_2:th.5">Th5</a></span>;<br/>
<a NAME="E10:16_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A10</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_1_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a></span>;<br/>
<a NAME="E11:16_1_1_1_1"/>
<font color="Maroon" title="c10">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="c12">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="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E5:16_1_1_1_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="partit_2.html#T5" target="_self" title="PARTIT_2:th.5">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:16_1_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:16_1_1_1_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" title="BVFUNC_1:def.16">BVFUNC_1:def 16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:16_1_1_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D16" title="BVFUNC_1:def.16">BVFUNC_1:def 16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:16_1_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D16" title="BVFUNC_1:def.16">BVFUNC_1:def 16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">given </span><font color="Maroon" title="c9">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font><span class="kw"> such that </span><a NAME="E3:16_1"/><span class="lab"><font color="Green" title="E18">A11</font></span>: 
<font color="Maroon" title="c9">x</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="c8">y</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
 <span class="kw">and </span><br/><a NAME="E4:16_1"/><span class="lab"><font color="Green" title="E19">A12</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c10">z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font><span class="kw"> such that </span><br/><a NAME="E6:16_1"/><span class="lab"><font color="Green" title="E20">A13</font></span>: 
<font color="Maroon" title="c10">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="c9">x</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">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
 <span class="kw">and </span><br/><a NAME="E7:16_1"/><span class="lab"><font color="Green" title="E21">A14</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:16_1"><span class="lab"><font color="Green" title="E19">A12</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" title="BVFUNC_1:def.16">BVFUNC_1:def 16</a></span>;<br/>
<a NAME="E8:16_1"/><span class="lab"><font color="Green" title="E22">A15</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">x</font>,<font color="Maroon" title="c8">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:16_1"><span class="lab"><font color="Green" title="E18">A11</font></span></a>, <a class="ref" href="partit_2.html#T5" target="_self" title="PARTIT_2:th.5">Th5</a></span>;<br/>
<a NAME="E9:16_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">z</font>,<font color="Maroon" title="c9">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E6:16_1"><span class="lab"><font color="Green" title="E20">A13</font></span></a>, <a class="ref" href="partit_2.html#T5" target="_self" title="PARTIT_2:th.5">Th5</a></span>;<br/>
<a NAME="E10:16_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">z</font>,<font color="Maroon" title="c8">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K4" title="RELSET_1:func.4">*</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E8:16_1"><span class="lab"><font color="Green" title="E22">A15</font></span></a>, <a class="ref" href="relat_1.html#D8" title="RELAT_1:def.8">RELAT_1:def 8</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E12:16_1"/><span class="lab"><font color="Green" title="E23">A16</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">z</font>,<font color="Maroon" title="c11">u</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E13:16_1"/><span class="lab"><font color="Green" title="E24">A17</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">u</font>,<font color="Maroon" title="c8">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p3"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c4">P</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D8" title="RELAT_1:def.8">RELAT_1:def 8</a></span>;<br/>
<a NAME="E14:16_1"/>
<font color="Maroon" title="c11">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="partit1.html#K4" title="PARTIT1:func.4">ERl</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K2" title="BVFUNC_2:func.2">'/\'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p4"><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">{</a><span class="default"><font color="Maroon" title="c5">Q</font></span><a href="bvfunc_2.html#K4" title="BVFUNC_2:func.4">}</a></span></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16_1"><span class="lab"><font color="Green" title="E23">A16</font></span></a>, <a class="ref" href="relat_1.html#T15" title="RELAT_1:th.15">RELAT_1:15</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">u</font> = <font color="Maroon" title="c11">u</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_1.html#T12" title="ORDERS_1:th.12">ORDERS_1:12</a></span>;<br/>
<a NAME="E16:16_1"/>
<font color="Maroon" title="c10">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="c12">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="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E12:16_1"><span class="lab"><font color="Green" title="E23">A16</font></span></a>, <a class="ref" href="partit_2.html#T5" target="_self" title="PARTIT_2:th.5">Th5</a></span>;<br/>
<a NAME="E17:16_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A18</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:16_1"><span class="lab"><font color="Green" title="E21">A14</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" title="BVFUNC_1:def.16">BVFUNC_1:def 16</a></span>;<br/>
<a NAME="E18:16_1"/>
<font color="Maroon" title="c12">u</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="c8">y</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">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E13:16_1"><span class="lab"><font color="Green" title="E24">A17</font></span></a>, <a class="ref" href="partit_2.html#T5" target="_self" title="PARTIT_2:th.5">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:16_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:16_1"><span class="lab"><font color="Green" title="E25">A18</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" title="BVFUNC_1:def.16">BVFUNC_1:def 16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">thus </span> <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>) = 
 <a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_2.html#D9" title="BVFUNC_2:def.9">BVFUNC_2:def 9</a></span>
<br/>.= 
 <a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_2.html#D9" title="BVFUNC_2:def.9">BVFUNC_2:def 9</a></span>
<br/>.= 
 <a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" title="BVFUNC_1:def.16">BVFUNC_1:def 16</a></span>
<br/>.= 
 <a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_2.html#D9" title="BVFUNC_2:def.9">BVFUNC_2:def 9</a></span>
<br/>.= 
 <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c3">G</font>)</span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c3">G</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_2.html#D9" title="BVFUNC_2:def.9">BVFUNC_2:def 9</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
