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<span class="kw">let </span><font color="Maroon" title="c1">B</font> be   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span><br/>



<a NAME="E1:79"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</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">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T47" title="LATTICES:th.47">LATTICES:47</a></span>;<br/>
<a NAME="E2:79"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<span class="p1">(<span class="default"><a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span></span>)</span> <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">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice2.html#T79" title="LATTICE2:th.79">LATTICE2:79</a></span>;<br/>
<a NAME="E3:79"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</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">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T48" title="LATTICES:th.48">LATTICES:48</a></span>;<br/>
<a NAME="E4:79"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span></span>)</span> <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">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice2.html#T78" title="LATTICE2:th.78">LATTICE2:78</a></span>;<br/>
<a NAME="E5:79"/><span class="kw">then </span>
 <a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#R2" title="LATTICES:pred.2">is_a_complement_of</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="lattices.html#D18" title="LATTICES:def.18">LATTICES:def 18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:79"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D21" title="LATTICES:def.21">LATTICES:def 21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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