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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">P</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="lattice4.html#M2">ClosedSubset</a> of <font color="Maroon">L</font>;<br/>



<b>consider </b><font color="Maroon">o1</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">P</font>, <font color="Maroon">o2</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">P</font><b> such that </b><br/><a NAME="E2:101"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L</font>) <a href="realset1.html#K1">||</a> <font color="Maroon">P</font> &amp; <font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">L</font>) <a href="realset1.html#K1">||</a> <font color="Maroon">P</font> &amp;  <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">o1</font>,<font color="Maroon">o2</font> #) )
 <b>by </b><i><a class="ref" href="filter_2.html#T5" target="_self">Th5</a></i>;<br/>
<b>consider </b><font color="Maroon">o3</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">P</font> <a href="filter_2.html#K10" target="_self">.:</a> , <font color="Maroon">o4</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">P</font> <a href="filter_2.html#K10" target="_self">.:</a> <b> such that </b><br/><a NAME="E4:101"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">o3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> ) <a href="realset1.html#K1">||</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="filter_2.html#K10" target="_self">.:</a> </span>)</span> &amp; <font color="Maroon">o4</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> ) <a href="realset1.html#K1">||</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="filter_2.html#K10" target="_self">.:</a> </span>)</span> &amp;  <a href="filter_2.html#K23" target="_self">latt</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="filter_2.html#K10" target="_self">.:</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="filter_2.html#K10" target="_self">.:</a> </span>)</span>,<font color="Maroon">o3</font>,<font color="Maroon">o4</font> #) )
 <b>by </b><i><a class="ref" href="filter_2.html#T5" target="_self">Th5</a></i>;<br/>
<b>thus </b><a NAME="E5:101"/>
 <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="filter_2.html#K23" target="_self">latt</a> <span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="lattice2.html#K1">.:</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="filter_2.html#K10" target="_self">.:</a> </span>)</span></span>)</span> <a href="filter_2.html#K24" target="_self">.:</a> 
 <b>by </b><i>, </i>;<br/>


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