<?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">a1</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">b1</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">a2</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">b2</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/>



<a NAME="E1:35"/>
for <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a2</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  holds <br/><span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</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="35_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/>

<b>assume </b><a NAME="E1:35_1"/><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a2</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/>

<i><font color="Green">E23</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a2</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a2</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</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"><font color="Maroon">a1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</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"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">a2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_4.html#T8">BVFUNC_4:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">a2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">b2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_4.html#T8">BVFUNC_4:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</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"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <font color="Maroon">b2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xboolean.html#K4">'&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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</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"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</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"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K4">'&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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</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"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</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"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K4">'&amp;'</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> <font color="Maroon">a2</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T17">BVFUNC_1:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</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"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K4">'&amp;'</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> <font color="Maroon">a2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="bvfunc_1.html#D7">BVFUNC_1:def 7</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:35_1_2"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><i><font color="Green">E30</font></i>: <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="bvfunc_1.html#K6">'or'</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font>
<b>by </b><i><a class="ref" href="bvfunc_1.html#T17">BVFUNC_1:17</a></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">a1</font></span>)</span> <a href="funct_2.html#K3">.</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"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span> <a href="funct_2.html#K3">.</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/><a NAME="E3:35_1_2"/><i><font color="Green">E31</font></i>: 
( <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  or <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a1</font></span>)</span> <a href="funct_2.html#K3">.</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="margrel1.html#T39">MARGREL1:39</a></i>;<br/><a NAME="E4:35_1_2"/>
( <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  or <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b1</font></span>)</span> <a href="funct_2.html#K3">.</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="margrel1.html#T39">MARGREL1:39</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a2</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a2</font></span>)</span> <a href="funct_2.html#K3">.</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"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="bvfunc_9.html#E1"><i><font color="Green">Lemma19</font></i></a>, , <a class="txt" href="bvfunc_9.html#E2"><i><font color="Green">Lemma21</font></i></a>, <a class="txt" href="bvfunc_9.html#E1:35_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="binarith.html#T22">BINARITH:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">a2</font></span>)</span> <a href="funct_2.html#K3">.</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"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></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"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <font color="Maroon">b2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></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"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></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"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span></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"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span> <a href="xboolean.html#K5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">b2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="margrel1.html#T46">MARGREL1:46</a></i>
<br/>.= 
<a href="margrel1.html#K7">FALSE</a>  <a href="xboolean.html#K5">'or'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K7">FALSE</a>  <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="margrel1.html#T46">MARGREL1:46</a></i>
<br/>.= 
 <a href="margrel1.html#K7">FALSE</a> 

;<br/><b>hence </b><a NAME="E6:35_1_2"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:35_1"/>
<span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</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>
<a NAME="E2:35"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a2</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#R1">'&lt;'</a>  <a href="valuat_1.html#K5">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="bvfunc_1.html#D15">BVFUNC_1:def 15</a></i>;<br/>
<b>hence </b><a NAME="E3:35"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">a2</font></span>)</span> <a href="valuat_1.html#K6">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">b1</font> <a href="bvfunc_1.html#K12">'imp'</a> <font color="Maroon">b2</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"><font color="Maroon">a2</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b2</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K12">'imp'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="valuat_1.html#K6">'&amp;'</a> <font color="Maroon">b1</font></span>)</span></span>)</span> <a href="funct_2.html#R2">=</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#T19">BVFUNC_1:19</a></i>;<br/>


</div>
