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<div><span class="kw">theorem </span><a NAME="T23"><span class="comment"><font color="firebrick">:: LATTICEA:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a>  <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  <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b3">P</font> where <font color="Olive" title="b3">P</font> is   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Olive" title="b1">L</font> : ( <font color="Olive" title="b3">P</font> is  <a href="filter_2.html#V2" title="FILTER_2:attr.2">prime</a>  &amp; <font color="Olive" title="b2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">P</font> ) </span> } </span> </div></div>
