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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a> <a href="lattices.html#V6" title="LATTICES:attr.6">meet-commutative</a> <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> <a href="robbins1.html#V6" title="ROBBINS1:attr.6">join-idempotent</a> <a href="sheffer1.html#V1" title="SHEFFER1:attr.1">upper-bounded'</a> <a href="sheffer1.html#V2" title="SHEFFER1:attr.2">lower-bounded'</a> <a href="sheffer1.html#V3" title="SHEFFER1:attr.3">distributive'</a> <a href="sheffer1.html#V4" title="SHEFFER1:attr.4">complemented'</a>  <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a> ;<br/>

<a NAME="E1:24"/>
 ex <font color="Olive" title="b1">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <br/>for <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">c</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon" title="c2">c</font> =  <a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font>;<br/>

<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 <font color="Maroon" title="c1">L</font>;<br/>

<b>thus </b><a NAME="E1:24_1"/>
( <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> )
 <b>by </b><i><a class="ref" href="sheffer1.html#T6" target="_self" title="SHEFFER1:th.6">Th6</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:24"/>
<font color="Maroon" title="c1">L</font> is <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a>
 <b>by </b><i><a class="ref" href="lattices.html#D13" title="LATTICES:def.13">LATTICES:def 13</a></i>;<br/>


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