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

<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>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:29"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:29"/>
<font color="Maroon">x</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/>

<a NAME="E3:29"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">q</font> where <font color="Olive">q</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Olive">q</font> </span>}</span> 
 
;<br/>
<a NAME="E4:29"/><b>then </b><i><font color="Green">E42</font></i>: 
 ex <font color="Olive">q</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">q</font> &amp; <font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Olive">q</font> )
 
;<br/>
<a NAME="E5:29"/>
<font color="Maroon">D</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3" target="_self">&lt;.</a><span class="default"><font color="Maroon">D</font></span><a href="filter_0.html#K3" target="_self">.)</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:29"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K3" target="_self">&lt;.</a><span class="default"><font color="Maroon">D</font></span><a href="filter_0.html#K3" target="_self">.)</a></span>
 <b>by </b><i>, , </i>;<br/>


</div>
