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<span class="kw">let </span><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</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">F1</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c1">L1</font><br/>  for <font color="Olive" title="b2">F2</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c2">L2</font>  st  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>, the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L1</font>, the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>, the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L2</font>, the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L2</font> #) &amp; <font color="Olive" title="b1">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F2</font> holds <br/> <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Olive" title="b1">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Olive" title="b2">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F1</font> be   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c1">L1</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">  for <font color="Olive" title="b1">F2</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c2">L2</font>  st  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>, the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L1</font>, the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>, the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L2</font>, the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L2</font> #) &amp; <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">F2</font> holds <br/> <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Olive" title="b1">F2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F2</font> be   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c2">L2</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="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>, the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L1</font>, the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>, the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L2</font>, the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L2</font> #) &amp; <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> implies  <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Maroon" title="c4">F2</font> )</span><br/>





<a NAME="E1:85"/>
 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="c3">F1</font> st <br/>( <font color="Olive" title="b1">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c3">F1</font> &amp; <font color="Olive" title="b2">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c3">F1</font> &amp;  <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Maroon" title="c3">F1</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="c3">F1</font>,<font color="Olive" title="b1">o1</font>,<font color="Olive" title="b2">o2</font> #) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#D9" onmouseover="rs('filter_0/D9')" onmouseout="rh()">FILTER_0:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:85"/>
(  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L1</font>, the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L1</font>, the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L2</font>, the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">L2</font>, the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">L2</font> #) &amp; <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> implies  <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K6" title="FILTER_0:func.6">latt</a> <font color="Maroon" title="c4">F2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#D9" onmouseover="rs('filter_0/D9')" onmouseout="rh()">FILTER_0:def 9</a></span>; <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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