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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="filter_0.html#NM2">I_Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="filter_0.html#M1">Filter</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K4" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><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 <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K4" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><a NAME="E1:29_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K4" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K9">Class</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K3" target="_self">/\/</a> <span class="p2">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> #)
 <b>by </b><i><a class="ref" href="filter_1.html#D5" target="_self">Def5</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:29_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="eqrel_1.html#T45">EQREL_1:45</a></i>;<br/><a NAME="E4:29_1"/>
<font color="Maroon">c<sub>1</sub></font> is   <a href="lattices.html#NM5">1_Lattice</a>
 <b>by </b><i><a class="ref" href="filter_0.html#T37">FILTER_0:37</a></i>;<br/><a NAME="E5:29_1"/><b>then </b><i><font color="Green">E24</font></i>: 
( <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="filter_1.html#E3:29_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="filter_1.html#D6" target="_self">Def6</a>, <a class="ref" href="lattices.html#T44">LATTICES:44</a></i>;<br/><b>hence </b><a NAME="E6:29_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="filter_1.html#T15" target="_self">Th15</a></i>;<br/><b>thus </b><a NAME="E7:29_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="filter_1.html#E5:29_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="filter_1.html#T15" target="_self">Th15</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:29"/>
<font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K4" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font> 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/>

<b>hence </b><a NAME="E3:29"/>
 <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="filter_1.html#K4" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="lattices.html#K6">Top</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="filter_1.html#K5" target="_self">/\/</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="filter_1.html#E1:29"><i><font color="Green">E22</font></i></a>, <a class="ref" href="lattices.html#D17">LATTICES:def 17</a></i>;<br/>


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