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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_Lattice</a>;<br/>

<b>given </b><font color="Maroon" title="c2">F</font> being    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E2:36"/><i><font color="Green" title="E26">A1</font></i>: 
( <font color="Maroon" title="c2">F</font> <a href="filter_0.html#NR1" title="FILTER_0:NR.1">is_ultrafilter</a>  &amp;  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> )
 ;<br/>

<a NAME="E3:36"/>
( <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">L</font></span><a href="filter_0.html#K1" title="FILTER_0:func.1">.)</a></span> &amp; <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="txt" href="lopclset.html#E2:36"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="filter_0.html#T32" title="FILTER_0:th.32">FILTER_0:32</a></i>;<br/>
<b>hence </b><a NAME="E4:36"/>
contradiction
 <b>by </b><i><a class="txt" href="lopclset.html#E2:36"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="filter_0.html#D4" title="FILTER_0:def.4">FILTER_0:def 4</a></i>;<br/>


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