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

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>given </b><font color="Maroon" title="c3">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E2:77"/><i><font color="Green" title="E55">A1</font></i>: 
for <font color="Olive" title="b1">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Maroon" title="c3">q</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp; <font color="Olive" title="b1">r</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D14" title="LATTICES:def.14">LATTICES:def 14</a><br/>

<a NAME="E3:77"/><i><font color="Green" title="E56">A2</font></i>: 
<font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a>
 
<b>by </b><i><a class="txt" href="filter_0.html#E2:77"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="lattices.html#D14" title="LATTICES:def.14">LATTICES:def 14</a></i>;<br/>
<a NAME="E4:77"/><b>then </b><i><font color="Green" title="E57">A3</font></i>: 
( <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font> &amp;  <a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> is   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a> )
 
<b>by </b><i><a class="txt" href="filter_0.html#E2:77"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="filter_0.html#T66" target="_self" title="FILTER_0:th.66">Th66</a>, <a class="ref" href="rlsub_2.html#T85" title="RLSUB_2:th.85">RLSUB_2:85</a></i>;<br/>
<a NAME="E5:77"/>
(  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> )
 
<b>by </b><i><a class="txt" href="filter_0.html#E3:77"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="filter_0.html#T12" target="_self" title="FILTER_0:th.12">Th12</a>, <a class="ref" href="filter_0.html#T63" target="_self" title="FILTER_0:th.63">Th63</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">q'</font> =  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</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" title="c5">r'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>;<br/><b>reconsider </b><font color="Maroon" title="c6">r</font> = <font color="Maroon" title="c5">r'</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> <b>by </b><i><a class="ref" href="filter_0.html#T63" target="_self" title="FILTER_0:th.63">Th63</a></i>;<br/><b>thus </b><font color="Maroon" title="c5">r'</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">q'</font> = 
<font color="Maroon" title="c3">q</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">r</font>
<b>by </b><i><a class="txt" href="filter_0.html#E4:77"><i><font color="Green" title="E57">A3</font></i></a>, <a class="ref" href="filter_0.html#T64" target="_self" title="FILTER_0:th.64">Th64</a></i>
<br/>.= 
<font color="Maroon" title="c4">q'</font>
<b>by </b><i><a class="txt" href="filter_0.html#E2:77"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="filter_0.html#E4:77"><i><font color="Green" title="E57">A3</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:77"/>
 <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="ref" href="rlsub_2.html#T85" title="RLSUB_2:th.85">RLSUB_2:85</a></i>;<br/>


</div>
