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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th32</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: FILTER_2:32</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> holds <br/> ( <font color="Olive" title="b2">I</font> is  <a href="filter_2.html#V1" title="FILTER_2:attr.1">max-ideal</a>  iff <font color="Olive" title="b2">I</font> <a href="filter_2.html#K3" title="FILTER_2:func.3">.:</a>  is  <a href="filter_0.html#V1" title="FILTER_0:attr.1">being_ultrafilter</a>  )</div></div>
