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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>let </b><font color="Maroon">Z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>







<b>assume </b><a NAME="E1:27"/>
<font color="Maroon">X</font> <a href="boolealg.html#K1" target="_self">\</a> <font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">Z</font>
 ;<br/>

<a NAME="E2:27"/><b>then </b>
<font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <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#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T1">FILTER_0:1</a></i>;<br/>
<a NAME="E3:27"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</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#K3">"\/"</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#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T31">LATTICES:31</a></i>;<br/>
<a NAME="E4:27"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">X</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">L</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T48">LATTICES:48</a></i>;<br/>
<a NAME="E5:27"/><b>then </b><i><font color="Green">E12</font></i>: 
<font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T43">LATTICES:43</a></i>;<br/>
<a NAME="E6:27"/>
<font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T22">LATTICES:22</a></i>;<br/>
<b>hence </b><a NAME="E7:27"/>
<font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Z</font>
 <b>by </b><i><a class="ref" href="boolealg.html#D4" target="_self">Def4</a>, <a class="ref" href="lattices.html#T25">LATTICES:25</a></i>;<br/>


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