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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM8">B_Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:79"/>
(  <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattice2.html#K1">.:</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="lattice2.html#T78">LATTICE2:78</a>, <a class="ref" href="lattice2.html#T79">LATTICE2:79</a>, <a class="ref" href="lattices.html#T47">LATTICES:47</a>, <a class="ref" href="lattices.html#T48">LATTICES:48</a></i>;<br/>
<a NAME="E2:79"/><b>then </b>
( <span class="p1">(<span class="default"><a href="filter_2.html#K6" target="_self">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><a href="filter_2.html#K6" target="_self">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="filter_2.html#K6" target="_self">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="filter_2.html#K6" target="_self">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="filter_2.html#K6" target="_self">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a>  &amp;  <a href="filter_2.html#K6" target="_self">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K7">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K7">`</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<a NAME="E3:79"/><b>then </b>
 <a href="filter_2.html#K6" target="_self">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#R2">is_a_complement_of</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="lattices.html#D18">LATTICES:def 18</a></i>;<br/>
<b>hence </b><a NAME="E4:79"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="filter_2.html#K5" target="_self">.:</a> </span>)</span> <a href="lattices.html#K7">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7">`</a> 
 <b>by </b><i><a class="ref" href="lattices.html#D21">LATTICES:def 21</a></i>;<br/>


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