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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V4">join-commutative</a> <a href="lattices.html#V6">meet-commutative</a> <a href="lattices.html#V11">distributive</a> <a href="robbins1.html#V6">join-idempotent</a> <a href="sheffer1.html#V1" target="_self">upper-bounded'</a> <a href="sheffer1.html#V2" target="_self">lower-bounded'</a> <a href="sheffer1.html#V3" target="_self">distributive'</a> <a href="sheffer1.html#V4" target="_self">complemented'</a>  <a href="lattices.html#L3">LattStr</a> ;<br/>

<a NAME="E1:22"/>
 ex <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>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="Olive">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> &amp; <font color="Olive">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">c</font> =  <a href="sheffer1.html#K1" target="_self">Top'</a> <font color="Maroon">L</font>;<br/>

<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>thus </b><a NAME="E1:22_1"/>
( <font color="Maroon">c</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:22"/>
<font color="Maroon">L</font> is <a href="lattices.html#V14">upper-bounded</a>
 <b>by </b><i><a class="ref" href="lattices.html#D14">LATTICES:def 14</a></i>;<br/>


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