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

<span class="kw">let </span><font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c2">w</font>, <font color="Maroon" title="c3">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:47_1"/>
( ( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  &amp; <font color="Maroon" title="c2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) or ( <font color="Maroon" title="c2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  &amp; <font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) or <font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  or <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" title="XBOOLEAN:def.3">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1"><span class="kw">suppose </span></a><a NAME="E1:47_1_1"/>
( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  &amp; <font color="Maroon" title="c2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/><div class="add"><a NAME="E2:47_1_1"/><span class="kw">then </span>
 <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T41" title="MARGREL1:th.41">MARGREL1:41</a></span>;<br/><a NAME="E3:47_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><a NAME="E4:47_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><span class="kw">hence </span><a NAME="E5:47_1_1"/>
 <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T41" title="MARGREL1:th.41">MARGREL1:41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_2"><span class="kw">suppose </span></a><span class="kw">that </span><a NAME="E1:47_1_2"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">and </span><br/><a NAME="E2:47_1_2"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/><div class="add"><a NAME="E3:47_1_2"/>
 <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_2"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="margrel1.html#T41" title="MARGREL1:th.41">MARGREL1:41</a></span>;<br/><a NAME="E4:47_1_2"/><span class="kw">then </span>
 <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1_2"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="margrel1.html#T41" title="MARGREL1:th.41">MARGREL1:41</a></span>;<br/><a NAME="E5:47_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><span class="kw">hence </span><a NAME="E6:47_1_2"/>
 <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T41" title="MARGREL1:th.41">MARGREL1:41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_3"><span class="kw">suppose </span></a><a NAME="E1:47_1_3"/>
<font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/><div class="add"><a NAME="E2:47_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><a NAME="E3:47_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><a NAME="E4:47_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><span class="kw">hence </span><a NAME="E5:47_1_3"/>
 <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T41" title="MARGREL1:th.41">MARGREL1:41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_4"><span class="kw">suppose </span></a><a NAME="E1:47_1_4"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/><div class="add"><a NAME="E2:47_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><a NAME="E3:47_1_4"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><a NAME="E4:47_1_4"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T45" title="MARGREL1:th.45">MARGREL1:45</a></span>;<br/><span class="kw">hence </span><a NAME="E5:47_1_4"/>
 <a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">w</font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">w</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">u</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T41" title="MARGREL1:th.41">MARGREL1:41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
