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

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font> being   <a href="filter_2.html#M2" title="FILTER_2:mode.2">Ideal</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1"><a href="filter_2.html#K19" title="FILTER_2:func.19">(.</a><span class="default"><font color="Olive" title="b1">I</font></span><a href="filter_2.html#K19" title="FILTER_2:func.19">.&gt;</a></span> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <font color="Olive" title="b1">I</font></span><br/><b>let </b><font color="Maroon" title="c2">I</font> be    <a href="filter_2.html#M2" title="FILTER_2:mode.2">Ideal</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="filter_2.html#K19" title="FILTER_2:func.19">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K19" title="FILTER_2:func.19">.&gt;</a></span> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <font color="Maroon" title="c2">I</font></span><br/>



<a NAME="E1:58"/>
( <span class="p1"><a href="filter_2.html#K19" title="FILTER_2:func.19">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K19" title="FILTER_2:func.19">.&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> &amp; <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="filter_2.html#K19" title="FILTER_2:func.19">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K19" title="FILTER_2:func.19">.&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="filter_2.html#D11" target="_self" title="FILTER_2:def.11">Def11</a></i>;<br/>
<b>hence </b><a NAME="E2:58"/>
<span class="p1"><a href="filter_2.html#K19" title="FILTER_2:func.19">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K19" title="FILTER_2:func.19">.&gt;</a></span> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <font color="Maroon" title="c2">I</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
