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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM2">D_Lattice</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:35"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:35"/><b>then </b>
(  not <font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">b</font> or  not <font color="Maroon">b</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>
<a NAME="E3:35"/><b>then </b>
(  ex <font color="Olive">F</font> being   <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">F</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K7" target="_self">F_primeSet</a> <font color="Maroon">L</font> &amp; not <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> ) or  ex <font color="Olive">F</font> being   <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">F</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K7" target="_self">F_primeSet</a> <font color="Maroon">L</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> ) )
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">F</font> being    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E5:35"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K7" target="_self">F_primeSet</a> <font color="Maroon">L</font> &amp; ( ( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> ) or ( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> &amp; not <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> ) ) )
 ;<br/>
<a NAME="E6:35"/>
( ( <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> &amp; not <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font> &amp; not <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> ) )
 
<b>by </b><i>, <a class="ref" href="openlatt.html#T1" target="_self">Th1</a></i>;<br/>
<b>hence </b><a NAME="E7:35"/>
<span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" target="_self">StoneH</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b</font>
 ;<br/>


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