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<b>let </b><font color="Maroon" title="c1">BL</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="lattices.html#NM8" title="LATTICES:NM.8">B_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">BL</font>;<br/><b>let </b><font color="Maroon" title="c4">F</font> be    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">BL</font>;<br/>







<b>assume </b><a NAME="E1:20"/>
<font color="Maroon" title="c4">F</font> <a href="filter_0.html#NR1" title="FILTER_0:NR.1">is_ultrafilter</a> 
 ;<br/>

<a NAME="E2:20"/><b>then </b>
( <font color="Maroon" title="c4">F</font> is <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</a> &amp; <font color="Maroon" title="c4">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="filter_0.html#K1" title="FILTER_0:func.1">&lt;.</a><span class="default"><font color="Maroon" title="c1">BL</font></span><a href="filter_0.html#K1" title="FILTER_0:func.1">.)</a></span> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T58" title="FILTER_0:th.58">FILTER_0:58</a></i>;<br/>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <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> iff ( <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="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> ) )
 <b>by </b><i><a class="ref" href="filter_0.html#D6" title="FILTER_0:def.6">FILTER_0:def 6</a></i>;<br/>


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