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

<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> =  <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>4</sub></font> = the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_1.html#D2" target="_self">FILTER_1:def 2</a><br/>

<b>assume </b><a NAME="E1:21"/>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:21"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K9">&lt;=&gt;</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D12">FILTER_0:def 12</a></i>;<br/>
<a NAME="E3:21"/><b>then </b><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a></i>;<br/>
<a NAME="E4:21"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>7</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a>, <a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>;<br/>
<a NAME="E5:21"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T2">FILTER_0:2</a></i>;<br/>
<a NAME="E6:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T4">FILTER_0:4</a></i>;<br/>
<a NAME="E7:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>;<br/>
<a NAME="E8:21"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="filter_1.html#E3:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a>, <a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a></i>;<br/>
<a NAME="E9:21"/><b>then </b><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T9">FILTER_0:9</a></i>;<br/>
<a NAME="E10:21"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a>, <a class="ref" href="lattices.html#D7">LATTICES:def 7</a></i>;<br/>
<a NAME="E11:21"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T2">FILTER_0:2</a></i>;<br/>
<a NAME="E12:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T4">FILTER_0:4</a></i>;<br/>
<a NAME="E13:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="lattices.html#D11">LATTICES:def 11</a></i>;<br/>
<a NAME="E14:21"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="lattices.html#R3">[=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="filter_1.html#E3:21"><i><font color="Green">E14</font></i></a>, <a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a>, <a class="ref" href="filter_0.html#D8">FILTER_0:def 8</a></i>;<br/>
<a NAME="E15:21"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="filter_0.html#K9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T9">FILTER_0:9</a></i>;<br/>
<a NAME="E16:21"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="filter_0.html#K9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font> &amp; the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="filter_1.html#E9:21"><i><font color="Green">E15</font></i></a>, <a class="ref" href="filter_0.html#D1">FILTER_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E17:21"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p2">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="filter_0.html#K11">equivalence_wrt</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="filter_0.html#D12">FILTER_0:def 12</a></i>;<br/>


</div>
