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<b>let </b><font color="Maroon">L1</font> be   <a href="lattices.html#NM1">Lattice</a>, <font color="Maroon">L2</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">F1</font> be    <a href="filter_2.html#M1" target="_self">Filter</a> of <font color="Maroon">L1</font>;<br/><b>let </b><font color="Maroon">F2</font> be    <a href="filter_2.html#M1" target="_self">Filter</a> of <font color="Maroon">L2</font>;<br/>





<b>consider </b><font color="Maroon">o1</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">F1</font>, <font color="Maroon">o2</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">F1</font><b> such that </b><br/><a NAME="E2:93"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L1</font> <a href="realset1.html#K1">||</a> <font color="Maroon">F1</font> &amp; <font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L1</font> <a href="realset1.html#K1">||</a> <font color="Maroon">F1</font> &amp;  <a href="filter_0.html#K8">latt</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <font color="Maroon">F1</font>,<font color="Maroon">o1</font>,<font color="Maroon">o2</font> #) )
 <b>by </b><i><a class="ref" href="filter_0.html#D10">FILTER_0:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">p1</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">F2</font>, <font color="Maroon">p2</font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">F2</font><b> such that </b><br/><a NAME="E4:93"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L2</font> <a href="realset1.html#K1">||</a> <font color="Maroon">F2</font> &amp; <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L2</font> <a href="realset1.html#K1">||</a> <font color="Maroon">F2</font> &amp;  <a href="filter_0.html#K8">latt</a> <font color="Maroon">F2</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <font color="Maroon">F2</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font> #) )
 <b>by </b><i><a class="ref" href="filter_0.html#D10">FILTER_0:def 10</a></i>;<br/>
<b>thus </b><a NAME="E5:93"/>
(  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L1</font> #) <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L2</font> #) &amp; <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> implies  <a href="filter_0.html#K8">latt</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a>  <a href="filter_0.html#K8">latt</a> <font color="Maroon">F2</font> )
 <b>by </b><i>, </i>;<br/>


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