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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>thus </b><a NAME="E1:46"/>
( <font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font> <a href="boolealg.html#R1" target="_self">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> implies <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">X</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:46_1"/>
<font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font> <a href="boolealg.html#R1" target="_self">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:46_1"/><b>then </b>
<font color="Maroon">X</font> <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="E3:46_1"/><b>then </b>
<font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <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>
 
<b>by </b><i><a class="ref" href="lattices.html#T27">LATTICES:27</a></i>;<br/>
<a NAME="E4:46_1"/><b>then </b><i><font color="Green">E12</font></i>: 
<font color="Maroon">X</font> <a href="lattices.html#R3">[=</a> <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>
 
<b>by </b><i><a class="ref" href="lattices.html#T18">LATTICES:18</a></i>;<br/>
<a NAME="E5:46_1"/>
<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">X</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T23">LATTICES:23</a></i>;<br/>
<b>hence </b><a NAME="E6:46_1"/>
<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">X</font>
 <b>by </b><i><a class="txt" href="boolealg.html#E21"><i><font color="Green">Lemma16</font></i></a>, </i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:46"/>
<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">X</font>
 ;<br/>

<a NAME="E3:46"/><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#K3">"\/"</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#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#T50">LATTICES:50</a></i>;<br/>
<a NAME="E4:46"/><b>then </b>
<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">X</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">Y</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> <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>
 
<b>by </b><i><a class="ref" href="lattices.html#T49">LATTICES:49</a></i>;<br/>
<a NAME="E5:46"/><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">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#K4">"/\"</a> <font color="Maroon">Y</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> <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>
 
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>;<br/>
<a NAME="E6:46"/><b>then </b>
<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"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> <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>
 
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>;<br/>
<a NAME="E7:46"/><b>then </b>
<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"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font></span>)</span> <a href="lattices.html#R3">[=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>;<br/>
<a NAME="E8:46"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T39">LATTICES:39</a></i>;<br/>
<a NAME="E9:46"/>
 <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T41">LATTICES:41</a></i>;<br/>
<b>hence </b><a NAME="E10:46"/>
<font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font> <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="txt" href="boolealg.html#E21"><i><font color="Green">Lemma16</font></i></a>, </i>;<br/>


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