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<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T60" target="_self" title="FILTER_2:th.60">Th61</a></span>;<br/>
<a NAME="E2:93_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>
 
;<br/>
<a NAME="E3:93_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A1</font></span>: 
( <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T61" target="_self" title="FILTER_2:th.61">Th62</a></span>;<br/>
<a NAME="E4:93_1_1"/>
<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="E5:93_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A2</font></span>: 
( <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T61" target="_self" title="FILTER_2:th.61">Th62</a></span>;<br/>
<a NAME="E6:93_1_1"/>
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T61" target="_self" title="FILTER_2:th.61">Th62</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:93_1_1"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E3:93_1_1"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="lattice2.html#T11" title="LATTICE2:th.11">LATTICE2:11</a></span>;<br/>
<span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_lat.html#D12" title="NAT_LAT:def.12">NAT_LAT:def 12</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">K</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">take </span>
<font color="Maroon" title="c3">o1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">take </span>
<font color="Maroon" title="c4">o2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">thus </span><a NAME="E9:93_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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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