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<b>let </b><font color="Maroon" title="c1">BL</font> be  non <a href="realset2.html#V3" title="REALSET2:attr.3">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> 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="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:16"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">F</font> where <font color="Olive" title="b1">F</font> is    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">BL</font> : ( <font color="Olive" title="b1">F</font> <a href="filter_0.html#NR1" title="FILTER_0:NR.1">is_ultrafilter</a>  &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> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">UF</font> being    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">BL</font><b> such that </b><br/><a NAME="E3:16"/><i><font color="Green" title="E18">A1</font></i>: 
( <font color="Maroon" title="c4">UF</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c4">UF</font> <a href="filter_0.html#NR1" title="FILTER_0:NR.1">is_ultrafilter</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">UF</font> )
 ;<br/>
<b>thus </b><a NAME="E4:16"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lopclset.html#K7" title="LOPCLSET:func.7">ultraset</a> <font color="Maroon" title="c1">BL</font>
 <b>by </b><i><a class="txt" href="lopclset.html#E3:16"><i><font color="Green" title="E18">A1</font></i></a></i>;<br/>


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