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<b>let </b><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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Olive" title="b2">q1</font> &amp; <font color="Olive" title="b3">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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/><b>let </b><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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Olive" title="b1">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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/><b>let </b><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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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/>











<b>assume </b><a NAME="E1:64"/><i><font color="Green" title="E42">A1</font></i>: 
( <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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c3">p1</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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/>

<b>thus </b><a NAME="E2:64"/>
( <font color="Maroon" title="c3">p1</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c6">q2</font> ) )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:64_1"/>
( <font color="Maroon" title="c3">p1</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c6">q2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_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/>

<a NAME="E2:64_1"/><b>then </b><i><font color="Green" title="E43">A2</font></i>: 
( <font color="Maroon" title="c3">p1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L1</font> &amp; <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#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c2">L2</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> )
 
<b>by </b><i><a class="ref" href="lattices.html#D18" title="LATTICES:def.18">LATTICES:def 18</a></i>;<br/>
<b>hence </b><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#K3" title="LATTICES:func.3">"\/"</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="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#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c2">L2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
<b>by </b><i><a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>
<br/>.= 
 <a href="lattices.html#K6" title="LATTICES:func.6">Top</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>
<b>by </b><i><a class="txt" href="#E1:64"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="filter_1.html#T44" target="_self" title="FILTER_1:th.44">Th44</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D18" title="LATTICES:def.18">LATTICES:def 18</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K1" title="LATTICES:func.1">"\/"</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</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> &amp; <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#K2" title="LATTICES:func.2">"/\"</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>  <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> &amp; <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#K2" title="LATTICES:func.2">"/\"</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> <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><br/>

<b>hence </b><a NAME="E4:64_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#K3" title="LATTICES:func.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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="lattices.html#K2" title="LATTICES:func.2">"/\"</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>  <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> &amp; <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#K2" title="LATTICES:func.2">"/\"</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> <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><br/>

<b>thus </b><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> = 
<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>
<b>by </b><i><a class="txt" href="#E2:64_1"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>
<br/>.= 
 <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>
<b>by </b><i><a class="txt" href="#E1:64"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="filter_1.html#T43" target="_self" title="FILTER_1:th.43">Th43</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K2" title="LATTICES:func.2">"/\"</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> <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><br/>

<b>hence </b><a NAME="E6:64_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="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="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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E3:64"/>
<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#R2" title="LATTICES:pred.2">is_a_complement_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">p1</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c6">q2</font> )</span><br/>

<a NAME="E4:64"/><b>then </b><i><font color="Green" title="E43">A3</font></i>: 
( <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#K3" title="LATTICES:func.3">"\/"</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>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</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> &amp; <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>  <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> )
 
<b>by </b><i><a class="ref" href="lattices.html#D18" title="LATTICES:def.18">LATTICES:def 18</a></i>;<br/>
<a NAME="E5:64"/>
<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#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c2">L2</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#K6" title="LATTICES:func.6">Top</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>
 
<b>by </b><i><a class="txt" href="#E1:64"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="filter_1.html#T44" target="_self" title="FILTER_1:th.44">Th44</a></i>;<br/>
<a NAME="E6:64"/><b>then </b><i><font color="Green" title="E44">A4</font></i>: 
<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#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L1</font></span>)</span>,<span class="p2">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c2">L2</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"><font color="Maroon" title="c3">p1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">q2</font></span>)</span></span><a href="filter_1.html#K9" title="FILTER_1:func.9">]</a></span>
 
<b>by </b><i><a class="txt" href="#E4:64"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>;<br/>
<a NAME="E7:64"/><b>then </b><i><font color="Green" title="E45">A5</font></i>: 
<font color="Maroon" title="c3">p1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L1</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E8:64"/>
<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> <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>
 
<b>by </b><i><a class="txt" href="#E1:64"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="filter_1.html#T43" target="_self" title="FILTER_1:th.43">Th43</a></i>;<br/>
<a NAME="E9:64"/><b>then </b><i><font color="Green" title="E46">A6</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="#E4:64"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>;<br/>
<a NAME="E10:64"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E11:64"/>
<font color="Maroon" title="c3">p1</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c4">q1</font>
 <b>by </b><i><a class="txt" href="#E7:64"><i><font color="Green" title="E45">A5</font></i></a>, <a class="ref" href="lattices.html#D18" title="LATTICES:def.18">LATTICES:def 18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c6">q2</font></span><br/>

<a NAME="E12:64"/><i><font color="Green" title="E47">A7</font></i>: 
<font color="Maroon" title="c5">p2</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c2">L2</font>
 
<b>by </b><i><a class="txt" href="#E6:64"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E13:64"/>
<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>
 
<b>by </b><i><a class="txt" href="#E9:64"><i><font color="Green" title="E46">A6</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E14:64"/>
<font color="Maroon" title="c5">p2</font> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c6">q2</font>
 <b>by </b><i><a class="txt" href="#E12:64"><i><font color="Green" title="E47">A7</font></i></a>, <a class="ref" href="lattices.html#D18" title="LATTICES:def.18">LATTICES:def 18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
