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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>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<i><font color="Green">E42</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T31" target="_self">Th31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p2">(<span class="default"><a href="lattices.html#K6" target="_self">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T48" target="_self">Th48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T43" target="_self">Th43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" target="_self">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T48" target="_self">Th48</a></i>
<br/>.= 
 <a href="lattices.html#K6" target="_self">Top</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D17" target="_self">Def17</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D7" target="_self">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D11" target="_self">Def11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#T47" target="_self">Th47</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T39" target="_self">Th39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4" target="_self">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D7" target="_self">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#T47" target="_self">Th47</a></i>
<br/>.= 
 <a href="lattices.html#K5" target="_self">Bottom</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D16" target="_self">Def16</a></i>
;<br/>
<a NAME="E3:68"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#R2" target="_self">is_a_complement_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="lattices.html#E1:68"><i><font color="Green">E42</font></i></a>, <a class="ref" href="lattices.html#D18" target="_self">Def18</a></i>;<br/>
<b>hence </b><a NAME="E4:68"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#K7" target="_self">`</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span> <a href="lattices.html#K3" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K7" target="_self">`</a> </span>)</span>
 <b>by </b><i><a class="ref" href="lattices.html#D21" target="_self">Def21</a></i>;<br/>


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