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

<span class="kw">let </span><font color="Maroon" title="c1">B</font> be   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">c</font>, <font color="Olive" title="b2">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Olive" title="b1">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Olive" title="b2">d</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Olive" title="b2">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Olive" title="b1">c</font> &amp; ( for <font color="Olive" title="b3">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font>  st <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Olive" title="b2">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Olive" title="b1">c</font> holds <br/><font color="Olive" title="b3">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b1">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Olive" title="b2">d</font></span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">c</font>, <font color="Maroon" title="c3">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font> &amp; ( for <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font>  st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font> holds <br/><font color="Olive" title="b1">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span> ) )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">A</font> =  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font>;<br/>
<a NAME="E1:83"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
<font color="Maroon" title="c1">B</font> is   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T40" title="FILTER_0:th.40">FILTER_0:40</a></span>;<br/>
<a NAME="E2:83"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
<font color="Maroon" title="c2">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T28" title="EQREL_1:th.28">EQREL_1:28</a></span>;<br/>
<a NAME="E3:83"/><span class="lab"><font color="Green" title="E59">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span>
 
;<br/>
<a NAME="E4:83"/><span class="lab"><font color="Green" title="E60">A4</font></span>: 
<font color="Maroon" title="c3">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span>
 
;<br/>
<a NAME="E5:83"/>
<font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T54" target="_self" title="FILTER_1:th.54">Th54</a></span>;<br/>
<a NAME="E6:83"/><span class="kw">then </span>
<font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E4:83"><span class="lab"><font color="Green" title="E60">A4</font></span></a>, <a class="txt" href="#E3:83"><span class="lab"><font color="Green" title="E59">A3</font></span></a>, <a class="txt" href="filter_1.html#E72"><span class="lab"><font color="Green" title="E54">Lm4</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:83"/>
<font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="ref" href="filter_1.html#T60" target="_self" title="FILTER_1:th.60">Th60</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font>  st <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font> holds <br/><font color="Olive" title="b1">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font> implies <font color="Maroon" title="c5">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E8:83"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="filter_0.html#K12" title="FILTER_0:func.12">equivalence_wrt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>,<font color="Maroon" title="c2">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span></span><br/>

<a NAME="E9:83"/><span class="kw">then </span>
<font color="Maroon" title="c5">b</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c3">d</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="filter_1.html#E72"><span class="lab"><font color="Green" title="E54">Lm4</font></span></a></span>;<br/>
<a NAME="E10:83"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A5</font></span>: 
<font color="Maroon" title="c3">d</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">b</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T18" title="FILTER_0:th.18">FILTER_0:18</a></span>;<br/>
<a NAME="E11:83"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T52" target="_self" title="FILTER_1:th.52">Th52</a></span>;<br/>
<a NAME="E12:83"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">d</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:83"><span class="lab"><font color="Green" title="E61">A5</font></span></a>, <a class="ref" href="lattices.html#T53" title="LATTICES:th.53">LATTICES:53</a></span>;<br/>
<a NAME="E13:83"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</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="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T27" title="LATTICES:th.27">LATTICES:27</a></span>;<br/>
<a NAME="E14:83"/><span class="lab"><font color="Green" title="E63">A7</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</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="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </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">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D11" title="LATTICES:def.11">LATTICES:def 11</a></span>;<br/>
<a NAME="E15:83"/><span class="lab"><font color="Green" title="E64">A8</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></span>;<br/>
<a NAME="E16:83"/><span class="lab"><font color="Green" title="E65">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T39" title="LATTICES:th.39">LATTICES:39</a></span>;<br/>
<a NAME="E17:83"/><span class="lab"><font color="Green" title="E66">A10</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T1" title="FILTER_0:th.1">FILTER_0:1</a>, <a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></span>;<br/>
<a NAME="E18:83"/><span class="lab"><font color="Green" title="E67">A11</font></span>: 
<font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T43" title="LATTICES:th.43">LATTICES:43</a></span>;<br/>
<a NAME="E19:83"/><span class="lab"><font color="Green" title="E68">A12</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</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="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D11" title="LATTICES:def.11">LATTICES:def 11</a></span>;<br/>
<a NAME="E20:83"/><span class="lab"><font color="Green" title="E69">A13</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T40" title="LATTICES:th.40">LATTICES:40</a></span>;<br/>
<a NAME="E21:83"/><span class="lab"><font color="Green" title="E70">A14</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">d</font></span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></span>;<br/>
<a NAME="E22:83"/><span class="lab"><font color="Green" title="E71">A15</font></span>: 
<font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">d</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D8" title="LATTICES:def.8">LATTICES:def 8</a></span>;<br/>
<a NAME="E23:83"/><span class="lab"><font color="Green" title="E72">A16</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">d</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_1.html#T51" target="_self" title="FILTER_1:th.51">Th51</a></span>;<br/>
<a NAME="E24:83"/><span class="lab"><font color="Green" title="E73">A17</font></span>: 
<font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T18" title="LATTICES:th.18">LATTICES:18</a></span>;<br/>
<a NAME="E25:83"/><span class="lab"><font color="Green" title="E74">A18</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T48" title="LATTICES:th.48">LATTICES:48</a></span>;<br/>
<a NAME="E26:83"/><span class="lab"><font color="Green" title="E75">A19</font></span>: 
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">c</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T47" title="LATTICES:th.47">LATTICES:47</a></span>;<br/>
<a NAME="E27:83"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</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="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></span>;<br/>
<a NAME="E28:83"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">d</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> </span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:83"><span class="lab"><font color="Green" title="E62">A6</font></span></a>, <a class="txt" href="#E24:83"><span class="lab"><font color="Green" title="E73">A17</font></span></a>, <a class="txt" href="#E14:83"><span class="lab"><font color="Green" title="E63">A7</font></span></a>, <a class="txt" href="#E16:83"><span class="lab"><font color="Green" title="E65">A9</font></span></a>, <a class="txt" href="#E15:83"><span class="lab"><font color="Green" title="E64">A8</font></span></a>, <a class="txt" href="#E26:83"><span class="lab"><font color="Green" title="E75">A19</font></span></a>, <a class="txt" href="#E20:83"><span class="lab"><font color="Green" title="E69">A13</font></span></a>, <a class="ref" href="filter_0.html#T1" title="FILTER_0:th.1">FILTER_0:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E29:83"/>
<font color="Maroon" title="c5">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">c</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c3">d</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:83"><span class="lab"><font color="Green" title="E68">A12</font></span></a>, <a class="txt" href="#E25:83"><span class="lab"><font color="Green" title="E74">A18</font></span></a>, <a class="txt" href="#E18:83"><span class="lab"><font color="Green" title="E67">A11</font></span></a>, <a class="txt" href="#E17:83"><span class="lab"><font color="Green" title="E66">A10</font></span></a>, <a class="txt" href="#E22:83"><span class="lab"><font color="Green" title="E71">A15</font></span></a>, <a class="txt" href="#E23:83"><span class="lab"><font color="Green" title="E72">A16</font></span></a>, <a class="txt" href="#E21:83"><span class="lab"><font color="Green" title="E70">A14</font></span></a>, <a class="ref" href="lattices.html#T25" title="LATTICES:th.25">LATTICES:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
