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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: FILTER_2:51</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="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <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="filter_2.html#K8" title="FILTER_2:func.8">"\/"</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></div></div>
