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

<b>let </b><font color="Maroon" title="c1">D1</font>, <font color="Maroon" title="c2">D2</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">g1</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D1</font>;<br/><b>let </b><font color="Maroon" title="c5">f2</font>, <font color="Maroon" title="c6">g2</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">D2</font>;<br/>











<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b><span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> $1,<span class="p1">(<span class="default"><span class="p2"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">g2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> $1,$2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1;<br/>
<b>thus </b><a NAME="E1:45"/>
( <font color="Maroon" title="c3">f1</font> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon" title="c4">g1</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <font color="Maroon" title="c6">g2</font> implies <span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="lattice2.html#R1" title="LATTICE2:pred.1">absorbs</a> <span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">g2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:45_1"/><i><font color="Green" title="E32">A1</font></i>: 
for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">b1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D1</font> holds  <font color="Maroon" title="c3">f1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">b1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice2.html#D1" title="LATTICE2:def.1">LATTICE2:def 1</a><br/>

<b>assume </b><a NAME="E2:45_1"/><i><font color="Green" title="E33">A2</font></i>: 
for <font color="Olive" title="b1">a2</font>, <font color="Olive" title="b2">b2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D2</font> holds  <font color="Maroon" title="c5">f2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a2</font>,<font color="Olive" title="b2">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice2.html#D1" title="LATTICE2:def.1">LATTICE2:def 1</a><br/>

<a NAME="E3:45_1"/><i><font color="Green" title="E34">A3</font></i>: 
for <font color="Olive" title="b1">d1</font>, <font color="Olive" title="b2">d1'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D1</font><br/> for <font color="Olive" title="b3">d2</font>, <font color="Olive" title="b4">d2'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D2</font> holds  <font color="Maroon">S<sub>1</sub></font>[<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">d1</font>,<font color="Olive" title="b3">d2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">d1'</font>,<font color="Olive" title="b4">d2'</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">a1</font>, <font color="Maroon" title="c8">b1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D1</font>;<br/><b>let </b><font color="Maroon" title="c9">a2</font>, <font color="Maroon" title="c10">b2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D2</font>;<br/>







<b>thus </b><span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p1">(<span class="default"><span class="p2"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">g2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">b1</font>,<font color="Maroon" title="c10">b2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span> = 
<span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c8">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">b2</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c8">b1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">b2</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">b2</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="txt" href="filter_1.html#E1:45_1"><i><font color="Green" title="E32">A1</font></i></a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="txt" href="filter_1.html#E2:45_1"><i><font color="Green" title="E33">A2</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<b>thus </b><a NAME="E4:45_1"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">D1</font>,<font color="Maroon" title="c2">D2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>]
 <b>from </b><i><a class="ref" href="filter_1.html#S5" target="_self" title="FILTER_1:sch.5">FILTER_1:sch 5</a>(<a class="txt" href="filter_1.html#E3:45_1"><i><font color="Green" title="E34">A3</font></i></a>);</i> <i><font color="Red">:: according to </font></i><a class="ref" href="lattice2.html#D1" title="LATTICE2:def.1">LATTICE2:def 1</a><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:45"/><i><font color="Green" title="E32">A4</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">D1</font>,<font color="Maroon" title="c2">D2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds  <span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><span class="p2"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">g2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice2.html#D1" title="LATTICE2:def.1">LATTICE2:def 1</a><br/>

<b>thus </b><a NAME="E3:45"/>
for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">b1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D1</font> holds  <font color="Maroon" title="c3">f1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">b1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a1</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="lattice2.html#D1" title="LATTICE2:def.1">LATTICE2:def 1</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">a1</font>, <font color="Maroon" title="c8">b1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D1</font>;<br/>



<b>consider </b><font color="Maroon" title="c9">a2</font>, <font color="Maroon" title="c10">b2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D2</font>;<br/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> = 
<span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p1">(<span class="default"><span class="p2"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">g2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">b1</font>,<font color="Maroon" title="c10">b2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="filter_1.html#E2:45"><i><font color="Green" title="E32">A4</font></i></a></i>
<br/>.= 
<span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c8">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">b2</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c8">b1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a2</font>,<font color="Maroon" title="c10">b2</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>
;<br/>
<b>hence </b><a NAME="E3:45_2"/>
<font color="Maroon" title="c3">f1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a1</font>,<font color="Maroon" title="c8">b1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a1</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c7">a2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D2</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice2.html#D1" title="LATTICE2:def.1">LATTICE2:def 1</a><br/><b>let </b><font color="Maroon" title="c8">b2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D2</font>;<br/>



<b>consider </b><font color="Maroon" title="c9">a1</font>, <font color="Maroon" title="c10">b1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D1</font>;<br/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> = 
<span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p1">(<span class="default"><span class="p2"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c4">g1</font>,<font color="Maroon" title="c6">g2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c8">b2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="filter_1.html#E2:45"><i><font color="Green" title="E32">A4</font></i></a></i>
<br/>.= 
<span class="p1"><a href="filter_1.html#K6" title="FILTER_1:func.6">|:</a><span class="default"><font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">f2</font></span><a href="filter_1.html#K6" title="FILTER_1:func.6">:|</a></span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">a2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a1</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="ref" href="filter_1.html#T22" target="_self" title="FILTER_1:th.22">Th22</a></i>
;<br/>
<b>hence </b><a NAME="E6:45"/>
<font color="Maroon" title="c5">f2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c8">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>


</div>
