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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="lattice4.html#NM2" title="LATTICE4:NM.2">ClosedSubset</a> of <font color="Maroon" title="c1">L</font> holds   <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<font color="Olive" title="b1">P</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">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="Olive" title="b1">P</font> <a href="filter_2.html#K3" title="FILTER_2:func.3">.:</a></span>)</span>)</span>)</span> <a href="filter_2.html#K11" title="FILTER_2:func.11">.:</a> </span><br/><span class="kw">let </span><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#NM2" title="LATTICE4:NM.2">ClosedSubset</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="filter_2.html#K10" title="FILTER_2:func.10">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#K10" title="FILTER_2:func.10">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#K3" title="FILTER_2:func.3">.:</a></span>)</span>)</span>)</span> <a href="filter_2.html#K11" title="FILTER_2:func.11">.:</a> </span><br/>



<a NAME="E1:92"/>
(  ex <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">P</font> st <br/>( <font color="Olive" title="b1">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="Olive" title="b2">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#K10" title="FILTER_2:func.10">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="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font> #) ) &amp;  ex <font color="Olive" title="b1">o3</font>, <font color="Olive" title="b2">o4</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="filter_2.html#K3" title="FILTER_2:func.3">.:</a></span>)</span> st <br/>( <font color="Olive" title="b1">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#K3" title="FILTER_2:func.3">.:</a></span>)</span> &amp; <font color="Olive" title="b2">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#K3" title="FILTER_2:func.3">.:</a></span>)</span> &amp;  <a href="filter_2.html#K10" title="FILTER_2:func.10">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#K3" title="FILTER_2:func.3">.:</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#K3" title="FILTER_2:func.3">.:</a></span>)</span>,<font color="Olive" title="b1">o3</font>,<font color="Olive" title="b2">o4</font> #) ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#D14" target="_self" onmouseover="rs('filter_2/D14')" onmouseout="rh()">Def14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:92"/>
 <a href="filter_2.html#K10" title="FILTER_2:func.10">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#K10" title="FILTER_2:func.10">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#K3" title="FILTER_2:func.3">.:</a></span>)</span>)</span>)</span> <a href="filter_2.html#K11" title="FILTER_2:func.11">.:</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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