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<div class="add">

<b>let </b><font color="Maroon">L</font> be  <a href="robbins1.html#V5" target="_self">Huntington</a> <a href="robbins1.html#V9" target="_self">de_Morgan</a> <a href="robbins1.html#NM1">preOrthoLattice</a>;<br/>

<b>reconsider </b><font color="Maroon">C</font> =  <a href="robbins1.html#K7" target="_self">Bot</a> <font color="Maroon">L</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E2:109"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <font color="Maroon">C</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp; <font color="Olive">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="109_1"><b>proof </b></a><div class="add">

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

<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<b>thus </b><font color="Maroon">C</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="robbins1.html#K7" target="_self">Bot</a> <font color="Maroon">L</font></span>)</span> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">a'</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">C</font>
<b>by </b><i/>
;<br/>

<b>hence </b><a NAME="E3:109_1"/>
<font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:109"/><b>then </b>
<font color="Maroon">L</font> is <a href="lattices.html#V13">lower-bounded</a>
 
<b>by </b><i><a class="ref" href="lattices.html#D13">LATTICES:def 13</a></i>;<br/>
<b>hence </b><a NAME="E4:109"/>
 <a href="robbins1.html#K7" target="_self">Bot</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="robbins1.html#T27" target="_self">Th27</a>, <a class="ref" href="lattices.html#D16">LATTICES:def 16</a></i>;<br/>


</div>
