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



<b>assume </b><a NAME="E1:25"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">L</font> is   <a href="lattices.html#NM4">0_Lattice</a> &amp; <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">L'</font> = <font color="Maroon">L</font> as   <a href="lattices.html#NM4">0_Lattice</a> ;<br/>
<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L'</font> ;<br/>
<a NAME="E4:25"/>
<font color="Maroon">p'</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5">Bottom</a> <font color="Maroon">L'</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L'</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T40">LATTICES:40</a></i>;<br/>
<a NAME="E5:25"/><b>then </b>
<span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<b>then consider </b><font color="Maroon">H</font> being    <a href="filter_0.html#M1" target="_self">Filter</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E7:25"/><i><font color="Green">E42</font></i>: 
( <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">H</font> &amp; <font color="Maroon">H</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  )
 <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">H</font>
;<br/>

<a NAME="E8:25"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">p</font></span><a href="filter_0.html#K2" target="_self">.)</a></span>
 
;<br/>
<b>hence </b><a NAME="E9:25"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> &amp; <font color="Maroon">H</font> <a href="filter_0.html#NR1" target="_self">is_ultrafilter</a>  )
 <b>by </b><i/>;<br/>


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