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<b>let </b><font color="Maroon" title="c3">p'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice4.html#D10" title="LATTICE4:def.10">LATTICE4:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>  holds <br/>(  not <font color="Maroon" title="c3">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  or ( <font color="Maroon" title="c3">p'</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  &amp; <font color="Maroon" title="c3">p'</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  ) )</span><br/><b>let </b><font color="Maroon" title="c4">q'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  or  not <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  or ( <font color="Maroon" title="c3">p'</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  &amp; <font color="Maroon" title="c3">p'</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  ) )</span><br/>



<a NAME="E1:29_1_1"/>
( <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S</font> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> ) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">L</font>) &amp;  <a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <font color="Maroon" title="c3">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p'</font> &amp;  <a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q'</font> &amp; <font color="Maroon" title="c3">p'</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <font color="Maroon" title="c3">p'</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <font color="Maroon" title="c4">q'</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <font color="Maroon" title="c3">p'</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="filter_2.html#K6" title="FILTER_2:func.6">.:</a> <font color="Maroon" title="c4">q'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p'</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">q'</font> )
 
;<br/>
<b>hence </b><a NAME="E2:29_1_1"/>
(  not <font color="Maroon" title="c3">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  or  not <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  or ( <font color="Maroon" title="c3">p'</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  &amp; <font color="Maroon" title="c3">p'</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  ) )
 <b>by </b><i><a class="ref" href="lattice4.html#D10" title="LATTICE4:def.10">LATTICE4:def 10</a></i>; <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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