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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM4">0_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="E1:22"/>
<font color="Maroon">X</font> <a href="boolealg.html#R3" target="_self">meets</a> <font color="Maroon">Y</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Z</font>
 ;<br/>

<a NAME="E2:22"/><b>then </b><i><font color="Green">E12</font></i>: 
<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#K4">"/\"</a> <font color="Maroon">Z</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:22"/><b>then </b><i><font color="Green">E13</font></i>: 
<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#K4">"/\"</a> <font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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="E4:22"/>
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Z</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="boolealg.html#D4" target="_self">Def4</a>, <a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>;<br/>
<a NAME="E5:22"/><b>then </b>
( <font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> &amp; <font color="Maroon">X</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> )
 
<b>by </b><i><a class="txt" href="boolealg.html#E5"><i><font color="Green">Lemma11</font></i></a>, <a class="ref" href="lattices.html#T40">LATTICES:40</a></i>;<br/>
<b>hence </b><a NAME="E6:22"/>
( <font color="Maroon">X</font> <a href="boolealg.html#R3" target="_self">meets</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">X</font> <a href="boolealg.html#R3" target="_self">meets</a> <font color="Maroon">Z</font> )
 <b>by </b><i/>;<br/>


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