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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: FILTER_2:57</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">B</font> being   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a><br/>  for <font color="Olive" title="b2">IB</font> being   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Olive" title="b1">B</font> holds <br/> ( ( <font color="Olive" title="b2">IB</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Olive" title="b1">B</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> &amp; <font color="Olive" title="b2">IB</font> is  <a href="filter_2.html#V2" title="FILTER_2:attr.2">prime</a>  ) iff <font color="Olive" title="b2">IB</font> is  <a href="filter_2.html#V1" title="FILTER_2:attr.1">max-ideal</a>  )</div></div>
