<?xml version="1.0"?>
<div class="add">

<b>reconsider </b><font color="Maroon">I</font> = <font color="Maroon">L</font> as   <a href="filter_0.html#NM2">I_Lattice</a> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">FI</font> = <font color="Maroon">F</font> as    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">I</font> ;<br/>
<b>reconsider </b><font color="Maroon">j</font> = the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">I</font>, <font color="Maroon">m</font> = the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">I</font> as   <a href="filter_1.html#NM4">BinOp</a> of  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font> <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">LL</font> =  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K9">Class</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="filter_1.html#K3" target="_self">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="filter_1.html#K3" target="_self">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">FI</font></span>)</span></span>)</span> #) as  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V3">strict</a>  <a href="lattices.html#L3">LattStr</a>  ;<br/>
<a NAME="E5:23_1_1"/>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>) is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>) is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L</font>) is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L</font>) is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>) <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L</font>) <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L</font>) )
 
<b>by </b><i><a class="ref" href="lattice2.html#T40">LATTICE2:40</a>, <a class="ref" href="lattice2.html#T41">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">LL</font>) is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">LL</font>) is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">LL</font>) is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">LL</font>) is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">LL</font>) <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">LL</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">LL</font>) <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">LL</font>) )
 
<b>by </b><i>, , </i>;<br/>
<b>then reconsider </b><font color="Maroon">LL</font> = <font color="Maroon">LL</font> as  <a href="lattices.html#V3">strict</a> <a href="lattices.html#NM1">Lattice</a> <b>by </b><i><a class="ref" href="lattice2.html#T17">LATTICE2:17</a></i>;<br/>
<b>take </b>
<font color="Maroon">LL</font>
;<br/>

<b>thus </b><a NAME="E8:23_1_1"/>
for <font color="Olive">R</font> being  <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>  st <font color="Olive">R</font> <a href="hidden.html#R1">=</a>  <a href="filter_0.html#K10">equivalence_wrt</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">LL</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K9">Class</a> <font color="Olive">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">R</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="filter_1.html#K3" target="_self">/\/</a> <font color="Olive">R</font></span>)</span> #)
 ;<br/>


</div>
