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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</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">p</font>, <font color="Olive" title="b2">q</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">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> &amp; <font color="Olive" title="b1">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> &amp; <font color="Olive" title="b2">q</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> )</span><br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> &amp; <font color="Maroon" title="c2">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> )</span><br/>





<a NAME="E1:48"/>
( <font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c2">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c3">q</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></i>;<br/>
<b>hence </b><a NAME="E2:48"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> &amp; <font color="Maroon" title="c2">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> &amp; <font color="Maroon" title="c3">q</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_2.html#K18" title="FILTER_2:func.18">(.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_2.html#K18" title="FILTER_2:func.18">.&gt;</a></span> )
 ; <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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