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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #);<br/>
<div><i><font color="Green">E59</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #);<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:82_1"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font> ;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E1:82_1"><i><font color="Green">E60</font></i></a>, <a class="ref" href="group_4.html#D12" target="_self">Def12</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="82_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #);<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:82_2"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font> ;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E1:82_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="group_4.html#D11" target="_self">Def11</a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #);<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="group_3.html#D1">GROUP_3:def 1</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>6</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E2:82"><i><font color="Green">E60</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>6</sub></font>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E2:82"><i><font color="Green">E60</font></i></a></i>
;<br/><a NAME="E3:82_3"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="group_4.html#E2:82"><i><font color="Green">E60</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E2:82"><i><font color="Green">E60</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_4.html#T75" target="_self">Th75</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="group_4.html#E2:82"><i><font color="Green">E60</font></i></a>, <a class="txt" href="group_4.html#E3:82_3"><i><font color="Green">E61</font></i></a></i>
;<br/><br/><a NAME="E5:82_3"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="group_4.html#E1:82"><i><font color="Green">E59</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E2:82"><i><font color="Green">E60</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="group_4.html#T84" target="_self">Th84</a></i>
;<br/><br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>7</sub></font> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E1:82"><i><font color="Green">E59</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E1:82"><i><font color="Green">E59</font></i></a></i>
;<br/><a NAME="E8:82_3"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="group_4.html#E1:82"><i><font color="Green">E59</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E1:82"><i><font color="Green">E59</font></i></a>, <a class="txt" href="group_4.html#E5:82_3"><i><font color="Green">E62</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="group_2.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_2.html#T102">GROUP_2:102</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K2">"/\"</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="group_4.html#E1:82"><i><font color="Green">E59</font></i></a>, <a class="txt" href="group_4.html#E8:82_3"><i><font color="Green">E63</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K2">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<font color="Maroon">c<sub>6</sub></font> <a href="group_2.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="group_4.html#E1:82"><i><font color="Green">E59</font></i></a>, <a class="txt" href="group_4.html#E3:82_3"><i><font color="Green">E61</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="group_4.html#T85" target="_self">Th85</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E4:82"/><b>then </b><i><font color="Green">E61</font></i>: 
(  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is <a href="lattices.html#V4">join-commutative</a> &amp;  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is <a href="lattices.html#V5">join-associative</a> &amp;  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is <a href="lattices.html#V8">meet-absorbing</a> &amp;  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is <a href="lattices.html#V6">meet-commutative</a> &amp;  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is <a href="lattices.html#V7">meet-associative</a> &amp;  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is <a href="lattices.html#V9">join-absorbing</a> )
 
<b>by </b><i><a class="ref" href="lattices.html#D4">LATTICES:def 4</a>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a>, <a class="ref" href="lattices.html#D6">LATTICES:def 6</a>, <a class="ref" href="lattices.html#D7">LATTICES:def 7</a>, <a class="ref" href="lattices.html#D8">LATTICES:def 8</a>, <a class="ref" href="lattices.html#D9">LATTICES:def 9</a></i>;<br/>
<b>hence </b><a NAME="E5:82"/>
 <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is   <a href="lattices.html#NM1">Lattice</a>
 <b>by </b><i><a class="ref" href="lattices.html#D10">LATTICES:def 10</a></i>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) as   <a href="lattices.html#NM1">Lattice</a> <b>by </b><i><a class="txt" href="group_4.html#E4:82"><i><font color="Green">E61</font></i></a>, <a class="ref" href="lattices.html#D10">LATTICES:def 10</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="group_3.html#D1">GROUP_3:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="group_3.html#D1">GROUP_3:def 1</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_2.html#K9">/\</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E1:82"><i><font color="Green">E59</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="group_2.html#T103">GROUP_2:103</a></i>
;<br/><b>hence </b><a NAME="E3:82_4"/>
<font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:82"/>
 <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is   <a href="lattices.html#NM4">0_Lattice</a>
 <b>by </b><i><a class="ref" href="lattices.html#D13">LATTICES:def 13</a></i>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="group_2.html#K6">(Omega).</a> <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="group_3.html#D1">GROUP_3:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="group_3.html#D1">GROUP_3:def 1</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="group_2.html#K6">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E2:82"><i><font color="Green">E60</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="group_4.html#T77" target="_self">Th77</a></i>
;<br/><b>hence </b><a NAME="E3:82_5"/>
<font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:82"/>
 <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="group_3.html#K1">Subgroups</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K9" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K10" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) is   <a href="lattices.html#NM5">1_Lattice</a>
 <b>by </b><i><a class="ref" href="lattices.html#D14">LATTICES:def 14</a></i>;<br/>


</div>
