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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/>





<b>assume </b><a NAME="E1:52"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">X</font> <a href="boolealg.html#K1" target="_self">\</a> <font color="Maroon">Y</font> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">Y</font> <a href="boolealg.html#K1" target="_self">\</a> <font color="Maroon">X</font>
 ;<br/>

<b>then </b><span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">X</font> = 
<font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>
<br/>.= 
<font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>
<br/>.= 
 <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
<b>by </b><i><a class="ref" href="lattices.html#T40">LATTICES:40</a></i>
;<br/>
<a NAME="E3:52"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">X</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="boolealg.html#R1" target="_self">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>;<br/>
<a NAME="E4:52"/><b>then </b>
<font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="boolealg.html#R1" target="_self">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T18">LATTICES:18</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<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="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">X</font> <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"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>
<br/>.= 
<font color="Maroon">X</font> <a href="lattices.html#K7">`</a> 
<b>by </b><i><a class="ref" href="lattices.html#D8">LATTICES:def 8</a></i>
;<br/>
<a NAME="E6:52"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</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#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">X</font> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T31">LATTICES:31</a></i>;<br/>
<a NAME="E7:52"/><b>then </b>
<span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">L</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span></span>)</span> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">X</font> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T48">LATTICES:48</a></i>;<br/>
<a NAME="E8:52"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">X</font> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T43">LATTICES:43</a></i>;<br/>
<a NAME="E9:52"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#D9">LATTICES:def 9</a></i>;<br/>
<a NAME="E10:52"/><b>then </b>
<font color="Maroon">Y</font> <a href="lattices.html#K7">`</a>  <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T21">LATTICES:21</a></i>;<br/>
<a NAME="E11:52"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K7">`</a>  <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T53">LATTICES:53</a></i>;<br/>
<a NAME="E12:52"/><b>then </b>
<font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T49">LATTICES:49</a></i>;<br/>
<a NAME="E13:52"/><b>then </b><i><font color="Green">E14</font></i>: 
<font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T49">LATTICES:49</a></i>;<br/>
<a NAME="E14:52"/>
<font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font></span>)</span> <a href="boolealg.html#R1" target="_self">=</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <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#K4">"/\"</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="boolealg.html#T27" target="_self">Th27</a>, <a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>;<br/>
<a NAME="E15:52"/><b>then </b>
<font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font></span>)</span> <a href="boolealg.html#R1" target="_self">=</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <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#K4">"/\"</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>;<br/>
<b>then </b> <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font>
<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#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font></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">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font>
<b>by </b><i><a class="ref" href="lattices.html#T18">LATTICES:18</a></i>
;<br/>
<a NAME="E17:52"/><b>then </b>
<font color="Maroon">X</font> <a href="lattices.html#K7">`</a>  <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T52">LATTICES:52</a></i>;<br/>
<a NAME="E18:52"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K7">`</a>  <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T53">LATTICES:53</a></i>;<br/>
<a NAME="E19:52"/><b>then </b>
<font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K7">`</a> 
 
<b>by </b><i><a class="ref" href="lattices.html#T49">LATTICES:49</a></i>;<br/>
<a NAME="E20:52"/><b>then </b>
<font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T49">LATTICES:49</a></i>;<br/>
<b>hence </b><a NAME="E21:52"/>
<font color="Maroon">X</font> <a href="boolealg.html#R1" target="_self">=</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="boolealg.html#T30" target="_self">Th30</a>, </i>;<br/>


</div>
