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

<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM2">D_Lattice</a>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:33"/><i><font color="Green">E18</font></i>: 
not <font color="Maroon">b</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font>
 ;<br/>

<b>set </b><font color="Maroon">A</font> = <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">b</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">a</font></span>)</span>;<br/>
<a NAME="E2:33"/><i><font color="Green">E19</font></i>: 
<span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">b</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:33"/>
for <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">b</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">a</font></span>)</span> &amp; <font color="Olive">Z</font> is <a href="ordinal1.html#V6">c=-linear</a> holds <br/> ex <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">b</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">a</font></span>)</span> &amp; ( for <font color="Olive">X1</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X1</font> <a href="hidden.html#R2">in</a> <font color="Olive">Z</font> holds <br/><font color="Olive">X1</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Y</font> ) )
 
<b>by </b><i><a class="ref" href="openlatt.html#D2" target="_self">Def2</a></i>;<br/>
<b>then consider </b><font color="Maroon">Y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:33"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">b</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">a</font></span>)</span> &amp; ( for <font color="Olive">Z</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">Z</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">b</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">a</font></span>)</span> &amp; <font color="Olive">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">Y</font> holds <br/> not <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Olive">Z</font> ) )
 <b>by </b><i>, <a class="ref" href="lattice4.html#T3">LATTICE4:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">Y</font> as    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font> <b>by </b><i>, </i>;<br/>
<a NAME="E7:33"/><i><font color="Green">E41</font></i>: 
( not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:33"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:33"/>
<font color="Maroon">Y</font> is <a href="filter_0.html#V2">prime</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_0.html#D6">FILTER_0:def 6</a><br/>

<b>thus </b><a NAME="E1:33_1"/>
(  not <font color="Maroon">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> or <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> or <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:33_1_1"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; not <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; not <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 ;<br/>

<b>set </b><font color="Maroon">F1</font> = <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span>;<br/>
<b>set </b><font color="Maroon">F2</font> = <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span>;<br/>
<a NAME="E2:33_1_1"/><i><font color="Green">E80</font></i>: 
(  not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> or  not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:33_1_1_1"/><i><font color="Green">E81</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> )
 ;<br/>

<b>then consider </b><font color="Maroon">c1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:33_1_1_1"/><i><font color="Green">E82</font></i>: 
( <font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">a1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c1</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="lattice4.html#T6">LATTICE4:6</a></i>;<br/>
<b>consider </b><font color="Maroon">c2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E5:33_1_1_1"/><i><font color="Green">E91</font></i>: 
( <font color="Maroon">c2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">a2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font> )
 <b>by </b><i>, <a class="ref" href="lattice4.html#T6">LATTICE4:6</a></i>;<br/>
<b>set </b><font color="Maroon">c</font> = <font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font>;<br/>
<a NAME="E6:33_1_1_1"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="txt" href="openlatt.html#E8"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="openlatt.html#T4" target="_self">Th4</a>, <a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a></i>;<br/>
<a NAME="E7:33_1_1_1"/>
( <font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c1</font> &amp; <font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c2</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T23">LATTICES:23</a></i>;<br/>
<a NAME="E8:33_1_1_1"/><b>then </b>
( <font color="Maroon">a1</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">a1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c1</font> &amp; <font color="Maroon">a2</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">a2</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T27">LATTICES:27</a></i>;<br/>
<a NAME="E9:33_1_1_1"/><b>then </b>
( <font color="Maroon">a1</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a2</font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font> )
 
<b>by </b><i><a class="txt" href="openlatt.html#E8"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="openlatt.html#T4" target="_self">Th4</a>, <a class="ref" href="lattices.html#T25">LATTICES:25</a></i>;<br/>
<a NAME="E10:33_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T6">FILTER_0:6</a></i>;<br/>
<a NAME="E11:33_1_1_1"/><b>then </b><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a2</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>;<br/>
<a NAME="E12:33_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a2</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c2</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="txt" href="openlatt.html#E7"><i><font color="Green">Lemma33</font></i></a>, , <a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E13:33_1_1_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="filter_0.html#T9">FILTER_0:9</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:33_1_1"/><i><font color="Green">E94</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> )
 
;<br/>
<a NAME="E4:33_1_1"/>
( <span class="p1"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> &amp; <span class="p1"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> )
 
<b>by </b><i><a class="ref" href="lattice4.html#T5">LATTICE4:5</a></i>;<br/>
<a NAME="E5:33_1_1"/><b>then </b><i><font color="Green">E95</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:33_1_1"/><i><font color="Green">E96</font></i>: 
( <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> &amp; <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> )
 
<b>by </b><i><a class="ref" href="lattice4.html#T5">LATTICE4:5</a></i>;<br/>
<a NAME="E7:33_1_1"/><b>then </b>
( <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a1</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">b</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">a</font></span>)</span> or <span class="p1"><a href="filter_0.html#K3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="filter_0.html#K2">&lt;.</a><span class="default"><font color="Maroon">a2</font></span><a href="filter_0.html#K2">.)</a></span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span></span><a href="filter_0.html#K3">.)</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">b</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" target="_self">SF_have</a> <font color="Maroon">a</font></span>)</span> )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E8:33_1_1"/>
contradiction
 <b>by </b><i>, <a class="txt" href="openlatt.html#E7"><i><font color="Green">Lemma33</font></i></a>, <a class="txt" href="openlatt.html#E8"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="openlatt.html#T4" target="_self">Th4</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:33_1"/>
( ( not <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; not <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> ) or <font color="Maroon">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 <b>by </b><i><a class="ref" href="filter_0.html#T10">FILTER_0:10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:33"/><b>then </b>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K7" target="_self">F_primeSet</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="openlatt.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E11:33"/>
 ex <font color="Olive">F</font> being   <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">F</font> <a href="hidden.html#R2">in</a>  <a href="openlatt.html#K7" target="_self">F_primeSet</a> <font color="Maroon">L</font> &amp; not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">F</font> )
 <b>by </b><i/>;<br/>


</div>
