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<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">b1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">b2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Olive" title="b3">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Olive" title="b4">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Olive" title="b4">b2</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Olive" title="b2">b1</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">b1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">b2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font></span><br/>



<a NAME="E1:135"/>
 for <font color="Olive" title="b1">z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  holds <br/><span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="135_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  implies <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  )</span><br/>

<span class="lab"><font color="Green" title="E32">A1</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D20" onmouseover="rs('margrel1/D20')" onmouseout="rh()">MARGREL1:def 20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D20" onmouseover="rs('margrel1/D20')" onmouseout="rh()">MARGREL1:def 20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T8" onmouseover="rs('bvfunc_4/T8')" onmouseout="rh()">BVFUNC_4:8</a></span>
<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="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_4.html#T8" onmouseover="rs('bvfunc_4/T8')" onmouseout="rh()">BVFUNC_4:8</a></span>
<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="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D4" onmouseover="rs('bvfunc_1/D4')" onmouseout="rh()">BVFUNC_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D4" onmouseover="rs('bvfunc_1/D4')" onmouseout="rh()">BVFUNC_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T14" onmouseover="rs('bvfunc_1/T14')" onmouseout="rh()">BVFUNC_1:14</a></span>
<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="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D4" onmouseover="rs('bvfunc_1/D4')" onmouseout="rh()">BVFUNC_1:def 4</a></span>
;<br/>
<span class="kw">assume </span><a NAME="E2:135_1"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="135_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> </span></a><div class="add"><a NAME="E1:135_1_2"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
( <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  or <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><a NAME="E2:135_1_2"/><span class="lab"><font color="Green" title="E35">A4</font></span>: 
( <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  or <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><span class="lab"><font color="Green" title="E36">A5</font></span>: <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="bvfunc_1.html#K5" title="BVFUNC_1:func.5">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T14" onmouseover="rs('bvfunc_1/T14')" onmouseout="rh()">BVFUNC_1:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c2">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c3">b1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D4" onmouseover="rs('bvfunc_1/D4')" onmouseout="rh()">BVFUNC_1:def 4</a></span>
;<br/><span class="kw">assume </span><a NAME="E4:135_1_2"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:135_1"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E3:135_1_2"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="txt" href="#E2:135_1_2"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="txt" href="#E1:135_1_2"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="ref" href="xboolean.html#T8" onmouseover="rs('xboolean/T8')" onmouseout="rh()">XBOOLEAN:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D19" onmouseover="rs('margrel1/D19')" onmouseout="rh()">MARGREL1:def 19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#D19" onmouseover="rs('margrel1/D19')" onmouseout="rh()">MARGREL1:def 19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K8" title="MARGREL1:func.8">'not'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">b2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
<a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> <a href="margrel1.html#K9" title="MARGREL1:func.9">'&amp;'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboolean.html#T138" onmouseover="rs('xboolean/T138')" onmouseout="rh()">XBOOLEAN:138</a></span>
<br/>.= 
 <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a> 

;<br/><span class="kw">hence </span><a NAME="E6:135_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:135_1"><span class="lab"><font color="Green" title="E33">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:135_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:135"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c4">a2</font></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b1</font> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">a2</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span></span>)</span> <a href="bvfunc_1.html#K9" title="BVFUNC_1:func.9">'imp'</a> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K1" title="BVFUNC_1:func.1">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="bvfunc_1.html#K2" title="BVFUNC_1:func.2">'&amp;'</a> <font color="Maroon" title="c3">b1</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">I_el</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#T16" onmouseover="rs('bvfunc_1/T16')" onmouseout="rh()">BVFUNC_1:16</a>, <a class="ref" href="bvfunc_1.html#D12" onmouseover="rs('bvfunc_1/D12')" onmouseout="rh()">BVFUNC_1:def 12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
