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<b>set </b><font color="Maroon" title="c2">US</font> = <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>  </span>}</span> ;<br/>
<b>consider </b><font color="Maroon" title="c3">p1</font>, <font color="Maroon" title="c4">p2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">BL</font><b> such that </b><br/><a NAME="E2:14_1_1"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c3">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">p2</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>;<br/>
<a NAME="E3:14_1_1"/>
( <font color="Maroon" title="c3">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">BL</font> or <font color="Maroon" title="c4">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">BL</font> )
 
<b>by </b><i><a class="txt" href="lopclset.html#E2:14_1_1"><i><font color="Green" title="E11">A1</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">BL</font><b> such that </b><br/><a NAME="E5:14_1_1"/><i><font color="Green" title="E12">A2</font></i>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">BL</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c6">H</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="E7:14_1_1"/><i><font color="Green" title="E13">A3</font></i>: 
( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">H</font> &amp; <font color="Maroon" title="c6">H</font> <a href="filter_0.html#NR1" title="FILTER_0:NR.1">is_ultrafilter</a>  )
 <b>by </b><i><a class="txt" href="lopclset.html#E5:14_1_1"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="filter_0.html#T24" title="FILTER_0:th.24">FILTER_0:24</a></i>;<br/>
<a NAME="E8:14_1_1"/>
<font color="Maroon" title="c6">H</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>  </span>}</span> 
 
<b>by </b><i><a class="txt" href="lopclset.html#E7:14_1_1"><i><font color="Green" title="E13">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:14_1_1"/>
not  <a href="lopclset.html#K7" title="LOPCLSET:func.7">ultraset</a> <font color="Maroon" title="c1">BL</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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