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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>





<b>assume </b><a NAME="E1:34"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 ;<br/>

<a NAME="E2:34"/><b>then </b>
(  not <font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">b</font> or  not <font color="Maroon" title="c3">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T26" title="LATTICES:th.26">LATTICES:26</a></i>;<br/>
<a NAME="E3:34"/><b>then </b>
(  ex <font color="Olive" title="b1">F</font> being   <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">L</font> &amp; not <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">F</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">F</font> ) or  ex <font color="Olive" title="b1">F</font> being   <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">L</font> &amp; not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">F</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">F</font> ) )
 
<b>by </b><i><a class="ref" href="openlatt.html#T22" target="_self" title="OPENLATT:th.22">Th22</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">F</font> being    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E5:34"/><i><font color="Green" title="E25">A1</font></i>: 
( <font color="Maroon" title="c4">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">L</font> &amp; ( ( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> &amp; not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> ) or <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> ) )
 ;<br/>
<b>thus </b><a NAME="E6:34"/>
 ex <font color="Olive" title="b1">F</font> being   <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">L</font> st <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="openlatt.html#K7" title="OPENLATT:func.7">F_primeSet</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="txt" href="openlatt.html#E5:34"><i><font color="Green" title="E25">A1</font></i></a></i>;<br/>


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