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<b>let </b><font color="Maroon">u</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K6">BOOLEAN</a> ;<br/><b>let </b><font color="Maroon">w</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K6">BOOLEAN</a> ;<br/><b>let </b><font color="Maroon">z</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="margrel1.html#K6">BOOLEAN</a> ;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1"/>
( ( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  &amp; <font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or ( <font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  &amp; <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  ) or <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  or <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a>  )
 </span><b>by </b><i><a class="ref" href="margrel1.html#T39">MARGREL1:39</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1"><b>suppose </b></a><b>that </b><a NAME="E1:41_1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>and </b><br/><a NAME="E2:41_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><div class="add"><a NAME="E3:41_1_1"/>
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a>, , <a class="txt" href="valuat_1.html#E2:41_1_1"><i><font color="Green">E30</font></i></a></i>;<br/><a NAME="E4:41_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/><a NAME="E5:41_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></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="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/><b>hence </b><a NAME="E6:41_1_1"/>
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></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="margrel1.html#K9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:41_1_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>and </b><br/><a NAME="E2:41_1_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><div class="add"><a NAME="E3:41_1_2"/>
 <a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i>, <a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/><a NAME="E4:41_1_2"/><b>then </b>
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i>, <a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/><a NAME="E5:41_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></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="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/><b>hence </b><a NAME="E6:41_1_2"/>
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></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="margrel1.html#K9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_3"><b>suppose </b></a><a NAME="E1:41_1_3"/>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 ;<br/><div class="add"><a NAME="E2:41_1_3"/><b>then </b>
<font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</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#T45">MARGREL1:45</a></i>;<br/><a NAME="E3:41_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/><a NAME="E4:41_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></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="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/><b>hence </b><a NAME="E5:41_1_3"/>
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></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="margrel1.html#K9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_4"><b>suppose </b></a><a NAME="E1:41_1_4"/>
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 ;<br/><div class="add"><a NAME="E2:41_1_4"/><b>then </b>
<font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</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#T45">MARGREL1:45</a></i>;<br/><a NAME="E3:41_1_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/><a NAME="E4:41_1_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></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="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K7">FALSE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T45">MARGREL1:45</a></i>;<br/><b>hence </b><a NAME="E5:41_1_4"/>
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">w</font></span>)</span></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="margrel1.html#K9">'not'</a> <span class="p4">(<span class="default"><font color="Maroon">w</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i><a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
