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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/>



<a NAME="E1:103"/>
 ex <font color="Olive">o1</font>, <font color="Olive">o2</font> being  <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">P</font> st <br/>( <font color="Olive">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="Olive">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="Olive">o1</font>,<font color="Olive">o2</font> #) )
 
<b>by </b><i><a class="ref" href="filter_2.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E2:103"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">P</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> &amp; the <a href="lattices.html#U2">L_join</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">P</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> <a href="realset1.html#K1">||</a> <font color="Maroon">P</font> &amp; the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">L</font>,<font color="Maroon">P</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="realset1.html#K1">||</a> <font color="Maroon">P</font> )
 ;<br/>


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