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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: FILTER_2:42</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> being   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b1">L</font> is  <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a>  &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Olive" title="b1">L</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> holds <br/>( <font color="Olive" title="b2">I</font> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Olive" title="b1">L</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> &amp; <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L</font> )</div></div>
