<?xml version="1.0"?>
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<b>let </b><font color="Maroon" title="c1">I</font> be   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">FI</font> be    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">I</font>;<br/>



<b>set </b><font color="Maroon" title="c3">R</font> =  <a href="filter_0.html#K11" title="FILTER_0:func.11">equivalence_wrt</a> <font color="Maroon" title="c2">FI</font>;<br/>
<b>set </b><font color="Maroon" title="c4">o</font> = the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">I</font>;<br/>
<b>let </b><font color="Maroon" title="c5">x1</font>, <font color="Maroon" title="c6">y1</font>, <font color="Maroon" title="c7">x2</font>, <font color="Maroon" title="c8">y2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">I</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_1.html#D2" target="_self" title="FILTER_1:def.2">FILTER_1:def 2</a><br/>

<b>assume </b><a NAME="E1:21"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">x1</font>,<font color="Maroon" title="c6">y1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="filter_0.html#K11" title="FILTER_0:func.11">equivalence_wrt</a> <font color="Maroon" title="c2">FI</font> &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">x2</font>,<font color="Maroon" title="c8">y2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="filter_0.html#K11" title="FILTER_0:func.11">equivalence_wrt</a> <font color="Maroon" title="c2">FI</font> )
 ;<br/>

<a NAME="E2:21"/><b>then </b>
( <font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c6">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> &amp; <font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> &amp; <font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c6">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> &amp; <font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D12" title="FILTER_0:def.12">FILTER_0:def 12</a></i>;<br/>
<a NAME="E3:21"/><b>then </b><i><font color="Green" title="E14">A1</font></i>: 
( <font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> &amp; <font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> &amp; <font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> &amp; <font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D1" title="FILTER_0:def.1">FILTER_0:def 1</a></i>;<br/>
<a NAME="E4:21"/>
( <font color="Maroon" title="c7">x2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c7">x2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span> &amp; <font color="Maroon" title="c5">x1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span> &amp; <font color="Maroon" title="c7">x2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span> &amp; <font color="Maroon" title="c5">x1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c6">y1</font> &amp; <font color="Maroon" title="c7">x2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c8">y2</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">FILTER_0:def 8</a>, <a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></i>;<br/>
<a NAME="E5:21"/><b>then </b>
( <font color="Maroon" title="c5">x1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c6">y1</font> &amp; <font color="Maroon" title="c7">x2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c8">y2</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T2" title="FILTER_0:th.2">FILTER_0:2</a></i>;<br/>
<a NAME="E6:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T4" title="FILTER_0:th.4">FILTER_0:4</a></i>;<br/>
<a NAME="E7:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font>
 
<b>by </b><i><a class="ref" href="lattices.html#D11" title="LATTICES:def.11">LATTICES:def 11</a></i>;<br/>
<a NAME="E8:21"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> )
 
<b>by </b><i><a class="txt" href="filter_1.html#E3:21"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="filter_0.html#D1" title="FILTER_0:def.1">FILTER_0:def 1</a>, <a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">FILTER_0:def 8</a></i>;<br/>
<a NAME="E9:21"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T9" title="FILTER_0:th.9">FILTER_0:9</a></i>;<br/>
<a NAME="E10:21"/>
( <font color="Maroon" title="c8">y2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">y2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span> &amp; <font color="Maroon" title="c6">y1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span> &amp; <font color="Maroon" title="c8">y2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span> &amp; <font color="Maroon" title="c6">y1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">x1</font> &amp; <font color="Maroon" title="c8">y2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c7">x2</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">FILTER_0:def 8</a>, <a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></i>;<br/>
<a NAME="E11:21"/><b>then </b>
( <font color="Maroon" title="c6">y1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">x1</font> &amp; <font color="Maroon" title="c8">y2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c7">x2</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T2" title="FILTER_0:th.2">FILTER_0:2</a></i>;<br/>
<a NAME="E12:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font>
 
<b>by </b><i><a class="ref" href="filter_0.html#T4" title="FILTER_0:th.4">FILTER_0:4</a></i>;<br/>
<a NAME="E13:21"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font>
 
<b>by </b><i><a class="ref" href="lattices.html#D11" title="LATTICES:def.11">LATTICES:def 11</a></i>;<br/>
<a NAME="E14:21"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">y2</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> )
 
<b>by </b><i><a class="txt" href="filter_1.html#E3:21"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="filter_0.html#D1" title="FILTER_0:def.1">FILTER_0:def 1</a>, <a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">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" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T9" title="FILTER_0:th.9">FILTER_0:9</a></i>;<br/>
<a NAME="E16:21"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font></span>)</span> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FI</font> &amp; the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c5">x1</font>,<font color="Maroon" title="c7">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">x2</font> &amp; the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c6">y1</font>,<font color="Maroon" title="c8">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y1</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c8">y2</font> )
 
<b>by </b><i><a class="txt" href="filter_1.html#E9:21"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="filter_0.html#D1" title="FILTER_0:def.1">FILTER_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E17:21"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c5">x1</font>,<font color="Maroon" title="c7">x2</font></span>)</span>,<span class="p2">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">I</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c6">y1</font>,<font color="Maroon" title="c8">y2</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="filter_0.html#K11" title="FILTER_0:func.11">equivalence_wrt</a> <font color="Maroon" title="c2">FI</font>
 <b>by </b><i><a class="ref" href="filter_0.html#D12" title="FILTER_0:def.12">FILTER_0:def 12</a></i>;<br/>


</div>
