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<b>reconsider </b><font color="Maroon" title="c3">o1</font> = <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>, <font color="Maroon" title="c4">o2</font> = <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> as   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">P</font> <b>by </b><i><a class="ref" href="filter_2.html#T61" target="_self" title="FILTER_2:th.61">Th61</a></i>;<br/>
<a NAME="E2:97_1_1"/>
( <font color="Maroon" title="c3">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="Maroon" title="c4">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> )
 
;<br/>
<a NAME="E3:97_1_1"/><b>then </b>
( <font color="Maroon" title="c3">o1</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon" title="c3">o1</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Maroon" title="c4">o2</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon" title="c4">o2</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Maroon" title="c3">o1</font> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon" title="c4">o2</font> &amp; <font color="Maroon" title="c4">o2</font> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon" title="c3">o1</font> )
 
<b>by </b><i><a class="ref" href="filter_2.html#T62" target="_self" title="FILTER_2:th.62">Th62</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">K</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font> #) as  <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> <b>by </b><i><a class="ref" href="lattice2.html#T17" title="LATTICE2:th.17">LATTICE2:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">K</font> = <font color="Maroon" title="c5">K</font> as  <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a>  <a href="nat_lat.html#M2" title="NAT_LAT:mode.2">Sublattice</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="nat_lat.html#D16" title="NAT_LAT:def.16">NAT_LAT:def 16</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">K</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  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> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <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> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <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="Maroon" title="c6">K</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> #) )</span><br/>

<b>take </b>
<font color="Maroon" title="c3">o1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">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="Maroon" title="c3">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">L</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Olive" title="b1">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">L</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c6">K</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="Maroon" title="c3">o1</font>,<font color="Olive" title="b1">o2</font> #) )</span><br/>

<b>take </b>
<font color="Maroon" title="c4">o2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">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">L</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c4">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">L</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c6">K</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="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font> #) )</span><br/>

<b>thus </b><a NAME="E6:97_1_1"/>
( <font color="Maroon" title="c3">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">L</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c4">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">L</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c2">P</font> &amp; <font color="Maroon" title="c6">K</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="Maroon" title="c3">o1</font>,<font color="Maroon" title="c4">o2</font> #) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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