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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:77"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D14">LATTICES:def 14</a><br/>

<a NAME="E2:77"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is   <a href="lattices.html#NM5">1_Lattice</a>
 
<b>by </b><i><a class="txt" href="filter_0.html#E1:77"><i><font color="Green">E54</font></i></a>, <a class="ref" href="lattices.html#D14">LATTICES:def 14</a></i>;<br/>
<a NAME="E3:77"/><b>then </b><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="filter_0.html#K8" target="_self">latt</a> <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K2" target="_self">.)</a></span> is   <a href="lattices.html#NM5">1_Lattice</a> )
 
<b>by </b><i><a class="txt" href="filter_0.html#E1:77"><i><font color="Green">E54</font></i></a>, <a class="ref" href="filter_0.html#T66" target="_self">Th66</a>, <a class="ref" href="rlsub_2.html#T85">RLSUB_2:85</a></i>;<br/>
<a NAME="E4:77"/>
(  <a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K2" target="_self">.)</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" target="_self">latt</a> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K2" target="_self">.)</a></span> )
 
<b>by </b><i><a class="txt" href="filter_0.html#E2:77"><i><font color="Green">E55</font></i></a>, <a class="ref" href="filter_0.html#T12" target="_self">Th12</a>, <a class="ref" href="filter_0.html#T63" target="_self">Th63</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" target="_self">latt</a> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><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 <span class="p1">(<span class="default"><a href="filter_0.html#K8" target="_self">latt</a> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="struct_0.html#M1">Element</a> of <span class="p1"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K2" target="_self">.)</a></span> <b>by </b><i><a class="ref" href="filter_0.html#T63" target="_self">Th63</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>4</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="filter_0.html#E3:77"><i><font color="Green">E56</font></i></a>, <a class="ref" href="filter_0.html#T64" target="_self">Th64</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="filter_0.html#E1:77"><i><font color="Green">E54</font></i></a>, <a class="txt" href="filter_0.html#E3:77"><i><font color="Green">E56</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:77"/>
 <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="filter_0.html#K8" target="_self">latt</a> <span class="p2"><a href="filter_0.html#K2" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="filter_0.html#K2" target="_self">.)</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="rlsub_2.html#T85">RLSUB_2:85</a></i>;<br/>


</div>
