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<b>reconsider </b><font color="Maroon" title="c3">I</font> = <font color="Maroon" title="c1">L</font> as   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a> <b>by </b><i><a class="txt" href="#E1:23"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">FI</font> = <font color="Maroon" title="c2">F</font> as    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c3">I</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">j</font> = the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c3">I</font>, <font color="Maroon" title="c6">m</font> = the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c3">I</font> as   <a href="filter_1.html#NM4" title="FILTER_1:NM.4">BinOp</a> of  <a href="filter_0.html#K11" title="FILTER_0:func.11">equivalence_wrt</a> <font color="Maroon" title="c4">FI</font> <b>by </b><i><a class="ref" href="filter_1.html#T13" target="_self" title="FILTER_1:th.13">Th13</a>, <a class="ref" href="filter_1.html#T14" target="_self" title="FILTER_1:th.14">Th14</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">LL</font> =  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11" title="FILTER_0:func.11">equivalence_wrt</a> <font color="Maroon" title="c4">FI</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11" title="FILTER_0:func.11">equivalence_wrt</a> <font color="Maroon" title="c4">FI</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">m</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11" title="FILTER_0:func.11">equivalence_wrt</a> <font color="Maroon" title="c4">FI</font></span>)</span></span>)</span> #) as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattices.html#V3" title="LATTICES:attr.3">strict</a>  <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a>  ;<br/>
<a NAME="E5:23_1_1"/>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">L</font>) is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">L</font>) is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">L</font>) is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">L</font>) is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">L</font>) <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">L</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">L</font>) <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">L</font>) )
 
<b>by </b><i><a class="ref" href="lattice2.html#T40" title="LATTICE2:th.40">LATTICE2:40</a>, <a class="ref" href="lattice2.html#T41" title="LATTICE2:th.41">LATTICE2:41</a></i>;<br/>
<a NAME="E6:23_1_1"/><b>then </b>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">LL</font>) is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">LL</font>) is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c7">LL</font>) is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c7">LL</font>) is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">LL</font>) <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c7">LL</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c7">LL</font>) <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c7">LL</font>) )
 
<b>by </b><i><a class="ref" href="filter_1.html#T4" target="_self" title="FILTER_1:th.4">Th4</a>, <a class="ref" href="filter_1.html#T5" target="_self" title="FILTER_1:th.5">Th5</a>, <a class="ref" href="filter_1.html#T12" target="_self" title="FILTER_1:th.12">Th12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">LL</font> = <font color="Maroon" title="c7">LL</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>take </b>
<font color="Maroon" title="c8">LL</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R</font> being  <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c8">LL</font> <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"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Olive" title="b1">R</font></span>)</span> #)</span><br/>

<b>thus </b><a NAME="E8:23_1_1"/>
for <font color="Olive" title="b1">R</font> being  <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c8">LL</font> <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"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">L</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Olive" title="b1">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">L</font> <a href="filter_1.html#K3" title="FILTER_1:func.3">/\/</a> <font color="Olive" title="b1">R</font></span>)</span> #)
 ; <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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