<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">B</font> be   <a href="lattices.html#NM8">B_Lattice</a>;<br/><b>let </b><font color="Maroon">FB</font> be    <a href="filter_0.html#M1" target="_self">Filter</a> of <font color="Maroon">B</font>;<br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">FB</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a> 
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">B</font>;<br/>

<b>thus </b><a NAME="E2:63"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FB</font> implies  not <font color="Maroon">a</font> <a href="lattices.html#K7">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">FB</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:63_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FB</font> &amp; <font color="Maroon">a</font> <a href="lattices.html#K7">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">FB</font> )
 ;<br/>

<a NAME="E2:63_1"/><b>then </b>
<font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="lattices.html#K7">`</a> </span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">FB</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:63_1"/><b>then </b>
(  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FB</font> &amp; <font color="Maroon">B</font> is   <a href="lattices.html#NM4">0_Lattice</a> )
 
<b>by </b><i><a class="ref" href="lattices.html#T47">LATTICES:47</a></i>;<br/>
<a NAME="E4:63_1"/><b>then </b>
<font color="Maroon">FB</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:63_1"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:63"/>
( not <font color="Maroon">a</font> <a href="lattices.html#K7">`</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">FB</font> implies <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">FB</font> )
 <b>by </b><i>, </i>;<br/>


</div>
