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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#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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span><br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span><br/>



<font color="Maroon" title="c2">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D4" target="_self" title="SHEFFER1:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sheffer1.html#K3" title="SHEFFER1:func.3">`#</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#T4" target="_self" title="SHEFFER1:th.4">Th4</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sheffer1.html#K3" title="SHEFFER1:func.3">`#</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D11" title="LATTICES:def.11">LATTICES:def 11</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sheffer1.html#K3" title="SHEFFER1:func.3">`#</a> </span>)</span>
<b>by </b><i><a class="ref" href="sheffer1.html#D4" target="_self" title="SHEFFER1:def.4">Def4</a></i>
<br/>.= 
 <a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="ref" href="sheffer1.html#T4" target="_self" title="SHEFFER1:th.4">Th4</a></i>
;<br/>
<b>hence </b><a NAME="E2:14"/>
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sheffer1.html#K2" title="SHEFFER1:func.2">Bot'</a> <font color="Maroon" title="c1">L</font>
 ; <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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