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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#V10" title="LATTICES:attr.10">Lattice-like</a> <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a>  <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a> ;<br/>

<a NAME="E1:25"/>
 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#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon" title="c2">c</font> =  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</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/>

<a NAME="E1:25_1"/>
<font color="Maroon" title="c2">c</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T41" title="LATTICES:th.41">LATTICES:41</a></i>;<br/>
<b>hence </b><a NAME="E2:25_1"/>
( <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="ref" href="lattices.html#D3" title="LATTICES:def.3">LATTICES:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:25"/>
<font color="Maroon" title="c1">L</font> is <a href="sheffer1.html#V2" title="SHEFFER1:attr.2">lower-bounded'</a>
 <b>by </b><i><a class="ref" href="sheffer1.html#D3" target="_self" title="SHEFFER1:def.3">Def3</a></i>;<br/>


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