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<b>let </b><font color="Maroon">c<sub>1</sub></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="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/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><a href="sheffer1.html#K2" target="_self">Bot'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K3" target="_self">`#</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#T4" target="_self">Th4</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sheffer1.html#K3" target="_self">`#</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="sheffer1.html#K1" target="_self">Top'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#T3" target="_self">Th3</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="sheffer1.html#D2" target="_self">Def2</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:18"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="sheffer1.html#V5" target="_self">meet-idempotent</a>
 <b>by </b><i><a class="ref" href="sheffer1.html#D9" target="_self">Def9</a></i>;<br/>


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