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

<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#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>, <font color="Olive" title="b2">b</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a><br/>  for <font color="Olive" title="b3">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="b4">PA</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">a</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Olive" title="b2">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font> holds <br/><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">PA</font>,<font color="Olive" title="b3">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">PA</font>,<font color="Olive" title="b3">G</font>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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">PA</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="c2">a</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font> holds <br/><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">PA</font>,<font color="Olive" title="b1">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b2">PA</font>,<font color="Olive" title="b1">G</font>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">PA</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="c2">a</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font> holds <br/><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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b1">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">PA</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font> implies <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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:26"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font></span><br/>

<a NAME="E2:26"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T10" target="_self" onmouseover="rs('bvfunc_4/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E3:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <font color="Maroon" title="c2">a</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T8" target="_self" onmouseover="rs('bvfunc_4/T8')" onmouseout="rh()">Th8</a></span>;<br/>
<a NAME="E4:26"/>
<font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="bvfunc_4.html#T10" target="_self" onmouseover="rs('bvfunc_4/T10')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E5:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E7">A3</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <font color="Maroon" title="c3">b</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T8" target="_self" onmouseover="rs('bvfunc_4/T8')" onmouseout="rh()">Th8</a></span>;<br/>
<a NAME="E6:26"/>
 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> holds  <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <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#K7" title="MARGREL1:func.7">TRUE</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> </span><br/>

<div><span class="lab"><font color="Green" title="E8">A4</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) &amp;  not <font color="Maroon" title="c3">b</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  ) implies <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )</span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26_1_1"/><span class="lab"><font color="Green" title="E9">A5</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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">and </span><br/><a NAME="E2:26_1_1"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) &amp;  not <font color="Maroon" title="c3">b</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> </span><br/><span class="kw">consider </span><font color="Maroon" title="c7">x1</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="E4:26_1_1"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
<font color="Maroon" title="c7">x1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>)
 <span class="kw">and </span><br/><a NAME="E5:26_1_1"/><span class="lab"><font color="Green" title="E12">A8</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a></span>;<br/><a NAME="E6:26_1_1"/><span class="lab"><font color="Green" title="E13">A9</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="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E4:26_1_1"><span class="lab"><font color="Green" title="E11">A7</font></span></a></span>;<br/><a NAME="E7:26_1_1"/><span class="lab"><font color="Green" title="E14">A10</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D4" onmouseover="rs('bvfunc_1/D4')" onmouseout="rh()">BVFUNC_1:def 4</a></span>
<br/>.= 
<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:26_1_1"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E6:26_1_1"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="ref" href="margrel1.html#D19" onmouseover="rs('margrel1/D19')" onmouseout="rh()">MARGREL1:def 19</a></span>
<br/>.= 
 <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 

;<br/><span class="kw">hence </span><a NAME="E9:26_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="ref" href="bvfunc_1.html#D11" onmouseover="rs('bvfunc_1/D11')" onmouseout="rh()">BVFUNC_1:def 11</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<div><span class="lab"><font color="Green" title="E9">A11</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) &amp;  not <font color="Maroon" title="c2">a</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  ) &amp; (  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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) holds <br/><font color="Maroon" title="c3">b</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  ) implies <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )</span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26_1_2"/><span class="lab"><font color="Green" title="E10">A12</font></span>: 
 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) &amp;  not <font color="Maroon" title="c2">a</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  )
 <span class="kw">and </span><br/><a NAME="E2:26_1_2"/><span class="lab"><font color="Green" title="E11">A13</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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) holds <br/><font color="Maroon" title="c3">b</font> <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#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> </span><br/><span class="kw">consider </span><font color="Maroon" title="c7">x1</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="E4:26_1_2"/><span class="lab"><font color="Green" title="E12">A14</font></span>: 
<font color="Maroon" title="c7">x1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>)
 <span class="kw">and </span><br/><a NAME="E5:26_1_2"/><span class="lab"><font color="Green" title="E13">A15</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="c7">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_2"><span class="lab"><font color="Green" title="E10">A12</font></span></a></span>;<br/><a NAME="E6:26_1_2"/><span class="lab"><font color="Green" title="E14">A16</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_2"><span class="lab"><font color="Green" title="E11">A13</font></span></a>, <a class="txt" href="#E4:26_1_2"><span class="lab"><font color="Green" title="E12">A14</font></span></a></span>;<br/><a NAME="E7:26_1_2"/><span class="lab"><font color="Green" title="E15">A17</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="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1_2"><span class="lab"><font color="Green" title="E13">A15</font></span></a>, <a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D4" onmouseover="rs('bvfunc_1/D4')" onmouseout="rh()">BVFUNC_1:def 4</a></span>
<br/>.= 
<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:26_1_2"><span class="lab"><font color="Green" title="E15">A17</font></span></a>, <a class="txt" href="#E6:26_1_2"><span class="lab"><font color="Green" title="E14">A16</font></span></a>, <a class="ref" href="margrel1.html#D19" onmouseover="rs('margrel1/D19')" onmouseout="rh()">MARGREL1:def 19</a></span>
<br/>.= 
 <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 

;<br/><span class="kw">hence </span><a NAME="E9:26_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="bvfunc_1.html#D11" onmouseover="rs('bvfunc_1/D11')" onmouseout="rh()">BVFUNC_1:def 11</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T7" target="_self" onmouseover="rs('bvfunc_4/T7')" onmouseout="rh()">Th7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T8" target="_self" onmouseover="rs('bvfunc_4/T8')" onmouseout="rh()">Th8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T8" target="_self" onmouseover="rs('bvfunc_4/T8')" onmouseout="rh()">Th8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T12" onmouseover="rs('bvfunc_1/T12')" onmouseout="rh()">BVFUNC_1:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T12" onmouseover="rs('bvfunc_1/T12')" onmouseout="rh()">BVFUNC_1:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T12" onmouseover="rs('bvfunc_1/T12')" onmouseout="rh()">BVFUNC_1:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K11" title="BVFUNC_1:func.11">O_el</a> <font color="Maroon" title="c1">Y</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T5" target="_self" onmouseover="rs('bvfunc_4/T5')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K11" title="BVFUNC_1:func.11">O_el</a> <font color="Maroon" title="c1">Y</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K11" title="BVFUNC_1:func.11">O_el</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T5" target="_self" onmouseover="rs('bvfunc_4/T5')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K11" title="BVFUNC_1:func.11">O_el</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T9" onmouseover="rs('bvfunc_1/T9')" onmouseout="rh()">BVFUNC_1:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T9" onmouseover="rs('bvfunc_1/T9')" onmouseout="rh()">BVFUNC_1:9</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E10">A18</font></span>: <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D4" onmouseover="rs('bvfunc_1/D4')" onmouseout="rh()">BVFUNC_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D20" onmouseover="rs('margrel1/D20')" onmouseout="rh()">MARGREL1:def 20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D20" onmouseover="rs('margrel1/D20')" onmouseout="rh()">MARGREL1:def 20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D19" onmouseover="rs('margrel1/D19')" onmouseout="rh()">MARGREL1:def 19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D19" onmouseover="rs('margrel1/D19')" onmouseout="rh()">MARGREL1:def 19</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E11">A19</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_5"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) &amp;  not <font color="Maroon" title="c2">a</font> <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#K7" title="MARGREL1:func.7">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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) &amp;  not <font color="Maroon" title="c3">b</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  ) implies <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )</span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26_1_5"/><span class="lab"><font color="Green" title="E12">A20</font></span>: 
 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) &amp;  not <font color="Maroon" title="c2">a</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  )
 <span class="kw">and </span><br/><a NAME="E2:26_1_5"/><span class="lab"><font color="Green" title="E13">A21</font></span>: 
 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) &amp;  not <font color="Maroon" title="c3">b</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> </span><br/><a NAME="E3:26_1_5"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" title="BVFUNC_1:func.16">B_INF</a> (<font color="Maroon" title="c3">b</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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_5"><span class="lab"><font color="Green" title="E13">A21</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" onmouseover="rs('bvfunc_1/D16')" onmouseout="rh()">BVFUNC_1:def 16</a></span>;<br/><span class="kw">hence </span><a NAME="E4:26_1_5"/>
<span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E10">A18</font></span></a>, <a class="txt" href="#E1:26_1_5"><span class="lab"><font color="Green" title="E12">A20</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" onmouseover="rs('bvfunc_1/D16')" onmouseout="rh()">BVFUNC_1:def 16</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_6"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  ) &amp; (  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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) holds <br/><font color="Maroon" title="c3">b</font> <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#K7" title="MARGREL1:func.7">TRUE</a>  ) implies <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )</span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26_1_6"/><span class="lab"><font color="Green" title="E12">A22</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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">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">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">and </span><br/><a NAME="E2:26_1_6"/><span class="lab"><font color="Green" title="E13">A23</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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bvfunc_1.html#K15" title="BVFUNC_1:func.15">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="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>) holds <br/><font color="Maroon" title="c3">b</font> <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#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> </span><br/><a NAME="E3:26_1_6"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K16" title="BVFUNC_1:func.16">B_INF</a> (<font color="Maroon" title="c3">b</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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_6"><span class="lab"><font color="Green" title="E13">A23</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" onmouseover="rs('bvfunc_1/D16')" onmouseout="rh()">BVFUNC_1:def 16</a></span>;<br/><span class="kw">hence </span><a NAME="E4:26_1_6"/>
<span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E10">A18</font></span></a>, <a class="txt" href="#E1:26_1_6"><span class="lab"><font color="Green" title="E12">A22</font></span></a>, <a class="ref" href="bvfunc_1.html#D16" onmouseover="rs('bvfunc_1/D16')" onmouseout="rh()">BVFUNC_1:def 16</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="E7:26_1"/>
<span class="p1">(<span class="default"><span class="p2">(<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E9">A11</font></span></a>, <a class="txt" href="#E5:26_1"><span class="lab"><font color="Green" title="E11">A19</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="E7:26"/>
<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">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="bvfunc_1.html#K10" title="BVFUNC_1:func.10">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c4">G</font>)</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D11" onmouseover="rs('bvfunc_1/D11')" onmouseout="rh()">BVFUNC_1:def 11</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
