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

<span class="kw">let </span><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</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">p1</font>, <font color="Olive" title="b2">q1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font><br/>  for <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">q2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> holds <br/>( ( <font color="Olive" title="b1">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Olive" title="b2">q1</font> &amp; <font color="Olive" title="b3">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Olive" title="b4">q2</font> ) iff <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Olive" title="b1">p1</font>,<font color="Olive" title="b3">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Olive" title="b2">q1</font>,<font color="Olive" title="b4">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p1</font>, <font color="Maroon" title="c4">q1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</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">  for <font color="Olive" title="b1">p2</font>, <font color="Olive" title="b2">q2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> holds <br/>( ( <font color="Maroon" title="c3">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Olive" title="b1">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Olive" title="b2">q2</font> ) iff <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Olive" title="b1">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Olive" title="b2">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">p2</font>, <font color="Maroon" title="c6">q2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</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"> ( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> implies ( ( <font color="Maroon" title="c3">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c6">q2</font> ) iff <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> ) )</span><br/>











<span class="kw">assume </span><a NAME="E1:66"/><span class="lab"><font color="Green" title="E27">A0</font></span>: 
( <font color="Maroon" title="c1">L1</font> is   <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</a> &amp; <font color="Maroon" title="c2">L2</font> is   <a href="lattices.html#NM6" title="LATTICES:NM.6">01_Lattice</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"> ( ( <font color="Maroon" title="c3">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c6">q2</font> ) iff <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">L</font> = <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:66"/>
( <font color="Maroon" title="c3">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c6">q2</font> implies <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</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"> ( <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> implies ( <font color="Maroon" title="c3">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c6">q2</font> ) )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:66_1"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
( <font color="Maroon" title="c3">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c6">q2</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"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">a</font> = <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">b</font> = <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>;<br/>
<a NAME="E2:66_1"/><span class="lab"><font color="Green" title="E29">a2</font></span>: 
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="filter_1.html#T35" onmouseover="rs('filter_1/T35')" onmouseout="rh()">FILTER_1:35</a></span>;<br/>
<a NAME="E3:66_1"/>
 for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span>  st <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> holds <br/><font color="Olive" title="b1">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</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"> ( <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span> implies <font color="Maroon" title="c10">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:66_1_1"/><span class="lab"><font color="Green" title="E30">Z1</font></span>: 
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</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"> <font color="Maroon" title="c10">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c11">x1</font>, <font color="Maroon" title="c12">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:66_1_1"/><span class="lab"><font color="Green" title="E31">Z2</font></span>: 
( <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font> &amp; <font color="Maroon" title="c12">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font> &amp; <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" onmouseover="rs('zfmisc_1/D2')" onmouseout="rh()">ZFMISC_1:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">x1</font> = <font color="Maroon" title="c11">x1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:66_1_1"><span class="lab"><font color="Green" title="E31">Z2</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">x2</font> = <font color="Maroon" title="c12">x2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:66_1_1"><span class="lab"><font color="Green" title="E31">Z2</font></span></a></span>;<br/>
<a NAME="E6:66_1_1"/>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c13">x1</font>,<font color="Maroon" title="c14">x2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T42" onmouseover="rs('filter_1/T42')" onmouseout="rh()">FILTER_1:42</a>, <a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E27">A0</font></span></a>, <a class="txt" href="#E3:66_1_1"><span class="lab"><font color="Green" title="E31">Z2</font></span></a>, <a class="txt" href="#E1:66_1_1"><span class="lab"><font color="Green" title="E30">Z1</font></span></a></span>;<br/>
<a NAME="E7:66_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">Z3</font></span>: 
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">q1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c13">x1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">q2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c14">x2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T35" onmouseover="rs('filter_1/T35')" onmouseout="rh()">FILTER_1:35</a></span>;<br/>
<a NAME="E8:66_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">T1</font></span>: 
<font color="Maroon" title="c4">q1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#T1" onmouseover="rs('xtuple_0/T1')" onmouseout="rh()">XTUPLE_0:1</a></span>;<br/>
<a NAME="E9:66_1_1"/><span class="lab"><font color="Green" title="E34">T2</font></span>: 
<font color="Maroon" title="c6">q2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c14">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:66_1_1"><span class="lab"><font color="Green" title="E32">Z3</font></span></a>, <a class="ref" href="xtuple_0.html#T1" onmouseover="rs('xtuple_0/T1')" onmouseout="rh()">XTUPLE_0:1</a></span>;<br/>
<a NAME="E10:66_1_1"/><span class="lab"><font color="Green" title="E35">Z4</font></span>: 
<font color="Maroon" title="c13">x1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:66_1_1"><span class="lab"><font color="Green" title="E33">T1</font></span></a>, <a class="txt" href="#E1:66_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a></span>;<br/>
<a NAME="E11:66_1_1"/>
<font color="Maroon" title="c14">x2</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66_1"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E9:66_1_1"><span class="lab"><font color="Green" title="E34">T2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:66_1_1"/>
<font color="Maroon" title="c10">x</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:66_1_1"><span class="lab"><font color="Green" title="E31">Z2</font></span></a>, <a class="ref" href="filter_1.html#T36" onmouseover="rs('filter_1/T36')" onmouseout="rh()">FILTER_1:36</a>, <a class="txt" href="#E10:66_1_1"><span class="lab"><font color="Green" title="E35">Z4</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="E4:66_1"/>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:66_1"><span class="lab"><font color="Green" title="E29">a2</font></span></a>, <a class="ref" href="filter_1.html#T42" onmouseover="rs('filter_1/T42')" onmouseout="rh()">FILTER_1:42</a>, <a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E27">A0</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">assume </span><a NAME="E3:66"/><span class="lab"><font color="Green" title="E28">W0</font></span>: 
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</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"> ( <font color="Maroon" title="c3">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c6">q2</font> )</span><br/>

<a NAME="E4:66"/><span class="kw">then </span>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E27">A0</font></span></a>, <a class="ref" href="filter_1.html#T42" onmouseover="rs('filter_1/T42')" onmouseout="rh()">FILTER_1:42</a></span>;<br/>
<a NAME="E5:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">w1</font></span>: 
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">q1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">q2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T35" onmouseover="rs('filter_1/T35')" onmouseout="rh()">FILTER_1:35</a></span>;<br/>
<a NAME="E6:66"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">W1</font></span>: 
( <font color="Maroon" title="c3">p1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xtuple_0.html#T1" onmouseover="rs('xtuple_0/T1')" onmouseout="rh()">XTUPLE_0:1</a></span>;<br/>
<a NAME="E7:66"/><span class="lab"><font color="Green" title="E31">w2</font></span>: 
 for <font color="Olive" title="b1">xx1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>  st <font color="Maroon" title="c4">q1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">xx1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font> holds <br/><font color="Olive" title="b1">xx1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">p1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">xx1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</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"> ( <font color="Maroon" title="c4">q1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">xx1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</font> implies <font color="Maroon" title="c8">xx1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">p1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:66_2"/>
<font color="Maroon" title="c4">q1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">xx1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L1</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"> <font color="Maroon" title="c8">xx1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">p1</font></span><br/>

<a NAME="E2:66_2"/><span class="kw">then </span>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">q1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">xx1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">q2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">p2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:66"><span class="lab"><font color="Green" title="E30">W1</font></span></a>, <a class="ref" href="filter_1.html#T42" onmouseover="rs('filter_1/T42')" onmouseout="rh()">FILTER_1:42</a>, <a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E27">A0</font></span></a></span>;<br/>
<a NAME="E3:66_2"/><span class="kw">then </span>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c8">xx1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T35" onmouseover="rs('filter_1/T35')" onmouseout="rh()">FILTER_1:35</a></span>;<br/>
<a NAME="E4:66_2"/><span class="kw">then </span>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c8">xx1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:66"><span class="lab"><font color="Green" title="E28">W0</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:66_2"/>
<font color="Maroon" title="c8">xx1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">p1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T36" onmouseover="rs('filter_1/T36')" onmouseout="rh()">FILTER_1:36</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>
<a NAME="E8:66"/>
 for <font color="Olive" title="b1">xx2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</font>  st <font color="Maroon" title="c6">q2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">xx2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font> holds <br/><font color="Olive" title="b1">xx2</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">p2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">xx2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L2</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"> ( <font color="Maroon" title="c6">q2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">xx2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</font> implies <font color="Maroon" title="c8">xx2</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">p2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:66_3"/>
<font color="Maroon" title="c6">q2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">xx2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c2">L2</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"> <font color="Maroon" title="c8">xx2</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">p2</font></span><br/>

<a NAME="E2:66_3"/><span class="kw">then </span>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">q1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">p1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">q2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">xx2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:66"><span class="lab"><font color="Green" title="E30">W1</font></span></a>, <a class="ref" href="filter_1.html#T42" onmouseover="rs('filter_1/T42')" onmouseout="rh()">FILTER_1:42</a>, <a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E27">A0</font></span></a></span>;<br/>
<a NAME="E3:66_3"/><span class="kw">then </span>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c4">q1</font>,<font color="Maroon" title="c6">q2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c8">xx2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1"><a href="filter_1.html#K7" title="FILTER_1:func.7">[:</a><span class="default"><font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font></span><a href="filter_1.html#K7" title="FILTER_1:func.7">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T35" onmouseover="rs('filter_1/T35')" onmouseout="rh()">FILTER_1:35</a></span>;<br/>
<a NAME="E4:66_3"/><span class="kw">then </span>
<span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c8">xx2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1"><a href="filter_1.html#K9" title="FILTER_1:func.9">[</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c5">p2</font></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:66"><span class="lab"><font color="Green" title="E28">W0</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:66_3"/>
<font color="Maroon" title="c8">xx2</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">p2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T36" onmouseover="rs('filter_1/T36')" onmouseout="rh()">FILTER_1:36</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="E9:66"/>
( <font color="Maroon" title="c3">p1</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c6">q2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:66"><span class="lab"><font color="Green" title="E31">w2</font></span></a>, <a class="txt" href="#E5:66"><span class="lab"><font color="Green" title="E29">w1</font></span></a>, <a class="ref" href="xtuple_0.html#T1" onmouseover="rs('xtuple_0/T1')" onmouseout="rh()">XTUPLE_0:1</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>
