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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM4">0_Lattice</a>;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font> being    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:37"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  &amp;  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:37"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_0.html#K1">&lt;.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_0.html#K1">.)</a></span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="lopclset.html#E1:37"><i><font color="Green">E32</font></i></a>, <a class="ref" href="filter_0.html#T32">FILTER_0:32</a></i>;<br/>
<b>hence </b><a NAME="E3:37"/>
contradiction
 <b>by </b><i><a class="txt" href="lopclset.html#E1:37"><i><font color="Green">E32</font></i></a>, <a class="ref" href="filter_0.html#D4">FILTER_0:def 4</a></i>;<br/>


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