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<div><span class="kw">theorem </span><a NAME="T49"><span class="comment"><font color="firebrick">:: FILTER_2:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a><br/>  for <font color="Olive" title="b2">I</font>, <font color="Olive" title="b3">J</font> being   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Olive" title="b1">L</font> holds  <span class="p1"><a href="filter_2.html#K7" title="FILTER_2:func.7">(.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">I</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">J</font></span>)</span></span><a href="filter_2.html#K7" title="FILTER_2:func.7">.&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">r</font> where <font color="Olive" title="b4">r</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> :  ex <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> st <br/>( <font color="Olive" title="b4">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b5">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b5">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> &amp; <font color="Olive" title="b6">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">J</font> ) </span> } </span> </div></div>
