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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM8">B_Lattice</a>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K3" target="_self">\+\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T51">LATTICES:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T18">LATTICES:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T40">LATTICES:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T39">LATTICES:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T18">LATTICES:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T40">LATTICES:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K1" target="_self">\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T39">LATTICES:39</a></i>
<br/>.= 
<font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">X</font>
<b>by </b><i><a class="ref" href="boolealg.html#T39" target="_self">Th39</a></i>
;<br/>
<b>hence </b><a NAME="E2:69"/>
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="boolealg.html#K3" target="_self">\+\</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#K3" target="_self">\+\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font>
 ;<br/>


</div>
