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<div><span class="kw">theorem </span><a NAME="T86"><span class="comment"><font color="firebrick">:: FILTER_2:86</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">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font> holds <br/> ( <font color="Olive" title="b2">S</font> is   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Olive" title="b1">L</font> iff  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> holds <br/> ( ( <font color="Olive" title="b3">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> &amp; <font color="Olive" title="b4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> ) iff <font color="Olive" title="b3">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> ) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="filter_2.html#E16"><span class="lab"><font color="Green" title="E7">Lm1</font></span></a></span>;<br/></div></div>
