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

<span class="kw">reconsider </span><font color="Maroon" title="c4">I</font> = <font color="Maroon" title="c1">L</font> as   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E16">A1</font></span></a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">c1</font>, <font color="Maroon" title="c6">c2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="filter_1.html#K4" title="FILTER_1:func.4">/\/</a> <font color="Maroon" title="c2">F</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K8" title="FILTER_0:func.8">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Olive" title="b1">R</font>,<font color="Maroon" title="c3">a</font>) ) &amp; (  for <font color="Olive" title="b1">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K8" title="FILTER_0:func.8">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c6">c2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Olive" title="b1">R</font>,<font color="Maroon" title="c3">a</font>) ) implies <font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:24_1_2"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 for <font color="Olive" title="b1">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K8" title="FILTER_0:func.8">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Olive" title="b1">R</font>,<font color="Maroon" title="c3">a</font>)
 <span class="kw">and </span><br/><a NAME="E3:24_1_2"/><span class="lab"><font color="Green" title="E18">A3</font></span>: 
 for <font color="Olive" title="b1">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="filter_0.html#K8" title="FILTER_0:func.8">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> holds <br/><font color="Maroon" title="c6">c2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Olive" title="b1">R</font>,<font color="Maroon" title="c3">a</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">FI</font> = <font color="Maroon" title="c2">F</font> as   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c4">I</font> ;<br/>
<a NAME="E5:24_1_2"/>
<font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K9" title="FILTER_0:func.9">equivalence_wrt</a> <font color="Maroon" title="c7">FI</font></span>)</span>,<font color="Maroon" title="c3">a</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_1_2"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:24_1_2"/>
<font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:24_1_2"><span class="lab"><font color="Green" title="E18">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
