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

<b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">Y</font>,<a href="margrel1.html#K6">BOOLEAN</a> , <font color="Maroon">b</font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">Y</font>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/><b>let </b><font color="Maroon">G</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="bvfunc_2.html#K1">PARTITIONS</a> <font color="Maroon">Y</font></span>)</span>;<br/><b>let </b><font color="Maroon">PA</font> be    <a href="eqrel_1.html#M1">a_partition</a> of <font color="Maroon">Y</font>;<br/>







<b>assume </b><a NAME="E1:26"/>
<font color="Maroon">a</font> <a href="bvfunc_1.html#K13">'eqv'</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K17">I_el</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E2:26"/><b>then </b>
( <font color="Maroon">a</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K17">I_el</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">b</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K17">I_el</a> <font color="Maroon">Y</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:26"/><b>then </b><i><font color="Green">E18</font></i>: 
( <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K17">I_el</a> <font color="Maroon">Y</font> &amp; <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K17">I_el</a> <font color="Maroon">Y</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:26"/><i><font color="Green">E20</font></i>: 
 <a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K21">B_INF</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="bvfunc_2.html#D9">BVFUNC_2:def 9</a></i>;<br/>
<a NAME="E5:26"/><i><font color="Green">E21</font></i>: 
 <a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K21">B_INF</a> <font color="Maroon">b</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="bvfunc_2.html#D9">BVFUNC_2:def 9</a></i>;<br/>
<a NAME="E6:26"/>
for <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

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

<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K12">'imp'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K12">'imp'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K12">'imp'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T15">BVFUNC_1:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T15">BVFUNC_1:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T15">BVFUNC_1:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K16">O_el</a> <font color="Maroon">Y</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K16">O_el</a> <font color="Maroon">Y</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K16">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K16">O_el</a> <font color="Maroon">Y</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T12">BVFUNC_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T12">BVFUNC_1:12</a></i>
;<br/>
<b>then </b><i><font color="Green">E23</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'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">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#D7">BVFUNC_1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xboolean.html#K5">'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">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="valuat_1.html#D6">VALUAT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xboolean.html#K5">'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">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="valuat_1.html#D6">VALUAT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xboolean.html#K3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xboolean.html#K4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xboolean.html#K5">'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">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="valuat_1.html#D5">VALUAT_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xboolean.html#K3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xboolean.html#K4">'&amp;'</a> <span class="p2">(<span class="default"><a href="xboolean.html#K3">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K5">'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">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="valuat_1.html#D5">VALUAT_1:def 5</a></i>
;<br/>
<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_1_3"/><i><font color="Green">E37</font></i>: 
( ( for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> holds <br/><font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) &amp; ( for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> holds <br/><font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) )
 ;<br/><a NAME="E2:26_1_3"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, <a class="ref" href="bvfunc_1.html#D19">BVFUNC_1:def 19</a></i>;<br/><a NAME="E3:26_1_3"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K21">B_INF</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, <a class="ref" href="bvfunc_1.html#D19">BVFUNC_1:def 19</a></i>;<br/><a NAME="E4:26_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E5:26_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E39</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_1_4"/><i><font color="Green">E40</font></i>: 
( ( for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> holds <br/><font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) &amp;  ex <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> &amp; not <font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) )
 ;<br/><b>then consider </b><font color="Maroon">x1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E3:26_1_4"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> &amp; <font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a>  )
 ;<br/><a NAME="E4:26_1_4"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i>, <a class="ref" href="margrel1.html#T43">MARGREL1:43</a></i>;<br/><a NAME="E5:26_1_4"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, </i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#D7">BVFUNC_1:def 7</a></i>
<br/>.= 
<a href="margrel1.html#K7">FALSE</a>  <a href="xboolean.html#K5">'or'</a> <a href="margrel1.html#K7">FALSE</a> 
<b>by </b><i>, , <a class="ref" href="valuat_1.html#D5">VALUAT_1:def 5</a></i>
<br/>.= 
 <a href="margrel1.html#K7">FALSE</a> 

;<br/><a NAME="E7:26_1_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><b>hence </b><a NAME="E8:26_1_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, <a class="ref" href="bvfunc_1.html#D14">BVFUNC_1:def 14</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E44</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_1_5"/><i><font color="Green">E45</font></i>: 
(  ex <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> &amp; not <font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) &amp; ( for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> holds <br/><font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) )
 ;<br/><b>then consider </b><font color="Maroon">x1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E3:26_1_5"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> &amp; <font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a>  )
 ;<br/><a NAME="E4:26_1_5"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i>, <a class="ref" href="margrel1.html#T43">MARGREL1:43</a></i>;<br/><a NAME="E5:26_1_5"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, </i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#D7">BVFUNC_1:def 7</a></i>
<br/>.= 
<a href="margrel1.html#K7">FALSE</a>  <a href="xboolean.html#K5">'or'</a> <a href="margrel1.html#K7">FALSE</a> 
<b>by </b><i>, , <a class="ref" href="valuat_1.html#D5">VALUAT_1:def 5</a></i>
<br/>.= 
 <a href="margrel1.html#K7">FALSE</a> 

;<br/><a NAME="E7:26_1_5"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">a</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><b>hence </b><a NAME="E8:26_1_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, <a class="ref" href="bvfunc_1.html#D14">BVFUNC_1:def 14</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_6"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_1_6"/><i><font color="Green">E49</font></i>: 
(  ex <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> &amp; not <font color="Maroon">a</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) &amp;  ex <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="bvfunc_1.html#K20">EqClass</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> &amp; not <font color="Maroon">b</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) )
 ;<br/><a NAME="E2:26_1_6"/><b>then </b><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i>, <a class="ref" href="bvfunc_1.html#D19">BVFUNC_1:def 19</a></i>;<br/><a NAME="E3:26_1_6"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K21">B_INF</a> <font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5">CompF</a> <font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i>, <a class="ref" href="bvfunc_1.html#D19">BVFUNC_1:def 19</a></i>;<br/><a NAME="E4:26_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E5:26_1_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:26_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p2">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:26"/>
<span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">a</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="bvfunc_1.html#K13">'eqv'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6">All</a> <font color="Maroon">b</font>,<font color="Maroon">PA</font>,<font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="bvfunc_1.html#K17">I_el</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="bvfunc_1.html#D14">BVFUNC_1:def 14</a></i>;<br/>


</div>
