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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">P</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="lattice4.html#M2" title="LATTICE4:mode.2">ClosedSubset</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>consider </b><font color="Maroon" title="c3">o1</font>, <font color="Maroon" title="c4">o2</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">P</font><b> such that </b><br/><a NAME="E2:101"/><i><font color="Green" title="E40">A1</font></i>: 
( <font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">L</font>) <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c4">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">L</font>) <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">P</font> &amp;  <a href="filter_2.html#K23" title="FILTER_2:func.23">latt</a> <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font> #) )
 <b>by </b><i><a class="ref" href="filter_2.html#D16" target="_self" title="FILTER_2:def.16">Def16</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">o3</font>, <font color="Maroon" title="c6">o4</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">P</font> <a href="filter_2.html#K10" title="FILTER_2:func.10">.:</a> <b> such that </b><br/><a NAME="E4:101"/><i><font color="Green" title="E41">A2</font></i>: 
( <font color="Maroon" title="c5">o3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> ) <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="filter_2.html#K10" title="FILTER_2:func.10">.:</a> </span>)</span> &amp; <font color="Maroon" title="c6">o4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> ) <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="filter_2.html#K10" title="FILTER_2:func.10">.:</a> </span>)</span> &amp;  <a href="filter_2.html#K23" title="FILTER_2:func.23">latt</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="filter_2.html#K10" title="FILTER_2:func.10">.:</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="filter_2.html#K10" title="FILTER_2:func.10">.:</a> </span>)</span>,<font color="Maroon" title="c5">o3</font>,<font color="Maroon" title="c6">o4</font> #) )
 <b>by </b><i><a class="ref" href="filter_2.html#D16" target="_self" title="FILTER_2:def.16">Def16</a></i>;<br/>
<b>thus </b><a NAME="E5:101"/>
 <a href="filter_2.html#K23" title="FILTER_2:func.23">latt</a> <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="filter_2.html#K23" title="FILTER_2:func.23">latt</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="filter_2.html#K10" title="FILTER_2:func.10">.:</a> </span>)</span></span>)</span> <a href="filter_2.html#K24" title="FILTER_2:func.24">.:</a> 
 <b>by </b><i><a class="txt" href="filter_2.html#E2:101"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="filter_2.html#E4:101"><i><font color="Green" title="E41">A2</font></i></a></i>;<br/>


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