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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: FILTER_1:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D1</font>, <font color="Olive" title="b2">D2</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">f1</font>, <font color="Olive" title="b4">g1</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b1">D1</font><br/>  for <font color="Olive" title="b5">f2</font>, <font color="Olive" title="b6">g2</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b2">D2</font> holds <br/> ( ( <font color="Olive" title="b3">f1</font> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Olive" title="b4">g1</font> &amp; <font color="Olive" title="b5">f2</font> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Olive" title="b6">g2</font> ) iff <span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Olive" title="b3">f1</font>,<font color="Olive" title="b5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Olive" title="b4">g1</font>,<font color="Olive" title="b6">g2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> )</div></div>
