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

<b>let </b><font color="Maroon">L1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="lattices.html#L3">LattStr</a> , <font color="Maroon">L2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="lattices.html#L3">LattStr</a> ;<br/>

<b>assume </b><a NAME="E1:54"/><i><font color="Green">E68</font></i>: 
<span class="p1"><a href="filter_1.html#K7" target="_self">[:</a><span class="default"><font color="Maroon">L1</font>,<font color="Maroon">L2</font></span><a href="filter_1.html#K7" target="_self">:]</a></span> is   <a href="lattices.html#NM1">Lattice</a>
 ;<br/>

<b>reconsider </b><font color="Maroon">LL</font> =  <a href="lattices.html#G3">LattStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="filter_1.html#K6" target="_self">|:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L1</font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L2</font>)</span><a href="filter_1.html#K6" target="_self">:|</a></span>,<span class="p1"><a href="filter_1.html#K6" target="_self">|:</a><span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L1</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L2</font>)</span><a href="filter_1.html#K6" target="_self">:|</a></span> #) as  non <a href="struct_0.html#V3">empty</a>  <a href="lattices.html#L3">LattStr</a>  ;<br/>
<a NAME="E3:54"/>
( <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>, <a class="ref" href="lattice2.html#T27">LATTICE2:27</a>, <a class="ref" href="lattice2.html#T29">LATTICE2:29</a>, <a class="ref" href="lattice2.html#T31">LATTICE2:31</a>, <a class="ref" href="lattice2.html#T32">LATTICE2:32</a>, <a class="ref" href="lattice2.html#T40">LATTICE2:40</a>, <a class="ref" href="lattice2.html#T41">LATTICE2:41</a></i>;<br/>
<a NAME="E4:54"/><b>then </b>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L1</font>) is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L1</font>) is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L1</font>) is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L1</font>) is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L1</font>) <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L1</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L1</font>) <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L1</font>) &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L2</font>) is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L2</font>) is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L2</font>) is <a href="binop_1.html#V1">commutative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L2</font>) is <a href="binop_1.html#V2">associative</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L2</font>) <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L2</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">L2</font>) <a href="lattice2.html#R1">absorbs</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">L2</font>) )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:54"/>
( <font color="Maroon">L1</font> is   <a href="lattices.html#NM1">Lattice</a> &amp; <font color="Maroon">L2</font> is   <a href="lattices.html#NM1">Lattice</a> )
 <b>by </b><i><a class="ref" href="lattice2.html#T17">LATTICE2:17</a></i>;<br/>


</div>
