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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1"><a href="filter_2.html#K7" title="FILTER_2:func.7">(.</a><span class="default"><font color="Olive" title="b1">I</font></span><a href="filter_2.html#K7" title="FILTER_2:func.7">.&gt;</a></span> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <font color="Olive" title="b1">I</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="filter_2.html#K7" title="FILTER_2:func.7">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K7" title="FILTER_2:func.7">.&gt;</a></span> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <font color="Maroon" title="c2">I</font></span><br/>



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( <span class="p1"><a href="filter_2.html#K7" title="FILTER_2:func.7">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K7" title="FILTER_2:func.7">.&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#K7" title="FILTER_2:func.7">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K7" title="FILTER_2:func.7">.&gt;</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#D9" target="_self" title="FILTER_2:def.9">Def11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:54"/>
<span class="p1"><a href="filter_2.html#K7" title="FILTER_2:func.7">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K7" title="FILTER_2:func.7">.&gt;</a></span> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <font color="Maroon" title="c2">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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