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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a> <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a> <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a>  <a href="robbins1.html#L2" title="ROBBINS1:struct.2">ComplLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="robbins1.html#K7" title="ROBBINS1:func.7">Bot</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="robbins1.html#K8" title="ROBBINS1:func.8">CLatt</a> <font color="Maroon" title="c1">L</font></span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c2">C</font> =  <a href="robbins1.html#K7" title="ROBBINS1:func.7">Bot</a> <font color="Maroon" title="c1">L</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="robbins1.html#K8" title="ROBBINS1:func.8">CLatt</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="ref" href="robbins1.html#D11" target="_self" title="ROBBINS1:def.11">Def11</a></i>;<br/>
<a NAME="E2:70"/>
for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="robbins1.html#K8" title="ROBBINS1:func.8">CLatt</a> <font color="Maroon" title="c1">L</font></span>)</span> holds <br/> ( <font color="Maroon" title="c2">C</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="robbins1.html#K8" title="ROBBINS1:func.8">CLatt</a> <font color="Maroon" title="c1">L</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font> &amp; <font color="Maroon" title="c3">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c4">a'</font> = <font color="Maroon" title="c3">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="robbins1.html#D11" target="_self" title="ROBBINS1:def.11">Def11</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">C</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><a href="robbins1.html#K7" title="ROBBINS1:func.7">Bot</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c4">a'</font>
<b>by </b><i><a class="ref" href="robbins1.html#D11" target="_self" title="ROBBINS1:def.11">Def11</a></i>
<br/>.= 
<font color="Maroon" title="c2">C</font>
<b>by </b><i><a class="ref" href="robbins1.html#D9" target="_self" title="ROBBINS1:def.9">Def9</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font></span><br/>

<b>hence </b><a NAME="E3:70_1"/>
<font color="Maroon" title="c3">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:70"/>
 <a href="robbins1.html#K7" title="ROBBINS1:func.7">Bot</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="robbins1.html#K8" title="ROBBINS1:func.8">CLatt</a> <font color="Maroon" title="c1">L</font></span>)</span>
 <b>by </b><i><a class="ref" href="lattices.html#D16" title="LATTICES:def.16">LATTICES:def 16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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