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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="realset2.html#V3">trivial</a> <a href="lattices.html#NM8">B_Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:20"/>
<font color="Maroon">c<sub>4</sub></font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a> 
 ;<br/>

<a NAME="E2:20"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> is <a href="filter_0.html#V2">prime</a> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T58">FILTER_0:58</a></i>;<br/>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> iff ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> ) )
 <b>by </b><i><a class="ref" href="filter_0.html#D6">FILTER_0:def 6</a></i>;<br/>


</div>
