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<b>let </b><font color="Maroon">BL</font> be  non <a href="realset2.html#V3">trivial</a> <a href="lattices.html#NM8">B_Lattice</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">BL</font>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">BL</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:19_1"/>
<font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="lopclset.html#K8" target="_self">UFilter</a> <font color="Maroon">BL</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 ;<br/><b>then consider </b><font color="Maroon">F0</font> being    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">BL</font><b> such that </b><br/><a NAME="E3:19_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">F0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> &amp; <font color="Maroon">F0</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F0</font> )
 <b>by </b><i><a class="ref" href="lopclset.html#T2" target="_self">Th2</a></i>;<br/><b>thus </b><a NAME="E4:19_1"/>
( <font color="Maroon">F</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> )
 <b>by </b><i><a class="ref" href="lopclset.html#T4" target="_self">Th4</a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:19"/>
( <font color="Maroon">F</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font> implies <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="lopclset.html#K8" target="_self">UFilter</a> <font color="Maroon">BL</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="lopclset.html#T2" target="_self">Th2</a></i>;<br/>


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