<?xml version="1.0"?>
<div class="add">

<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>thus </b><a NAME="E1:19"/>
( <font color="Maroon">X</font> <a href="lattices.html#K3">"\/"</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#R1" target="_self">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> &amp; <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> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1"/><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="boolealg.html#R1" target="_self">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:19_1"/><b>then </b><i><font color="Green">E13</font></i>: 
( <font color="Maroon">X</font> <a href="lattices.html#R3">[=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> &amp;  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">X</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T22">LATTICES:22</a>, <a class="ref" href="lattices.html#T41">LATTICES:41</a></i>;<br/>
<a NAME="E3:19_1"/>
( <font color="Maroon">Y</font> <a href="lattices.html#R3">[=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> &amp;  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">Y</font> )
 
<b>by </b><i>, <a class="ref" href="lattices.html#T22">LATTICES:22</a>, <a class="ref" href="lattices.html#T41">LATTICES:41</a></i>;<br/>
<b>hence </b><a NAME="E4:19_1"/>
( <font color="Maroon">X</font> <a href="boolealg.html#R1" target="_self">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> &amp; <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="ref" href="boolealg.html#D3" target="_self">Def3</a>, </i>;<br/>


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

<b>thus </b><a NAME="E2:19"/>
( <font color="Maroon">X</font> <a href="boolealg.html#R1" target="_self">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> &amp; <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="lattices.html#K3">"\/"</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="ref" href="lattices.html#T39">LATTICES:39</a></i>;<br/>


</div>
