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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">Z</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">W</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be   <a href="fuzzy_3.html#NM1">RMembership_Func</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">S</font> be   <a href="fuzzy_3.html#NM1">RMembership_Func</a> of <font color="Maroon">Y</font>,<font color="Maroon">Z</font>;<br/><b>let </b><font color="Maroon">T</font> be   <a href="fuzzy_3.html#NM1">RMembership_Func</a> of <font color="Maroon">Z</font>,<font color="Maroon">W</font>;<br/>







<a NAME="E1:64"/><i><font color="Green">E41</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">W</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">W</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="fuzzy_1.html#D1">FUZZY_1:def 1</a></i>;<br/>
<a NAME="E2:64"/>
for <font color="Olive">x</font>, <font color="Olive">w</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Olive">x</font>,<font color="Olive">w</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Olive">x</font>,<font color="Olive">w</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">w</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:64_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> ;<br/>
<b>reconsider </b><font color="Maroon">w</font> = <font color="Maroon">w</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> <b>by </b><i/>;<br/>
<a NAME="E4:64_1"/><i><font color="Green">E48</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">A</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ;<br/>
<b>set </b><font color="Maroon">B</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ;<br/>
<a NAME="E5:64_1"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span>  iff <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:64_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">z</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font><b> such that </b><br/><a NAME="E3:64_1_1_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span>
 ;<br/><a NAME="E4:64_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">z</font>,<font color="Maroon">w</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:64_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> 
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:64_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">z</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font><b> such that </b><br/><a NAME="E4:64_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">z</font>,<font color="Maroon">w</font></span>)</span>
 ;<br/>
<a NAME="E5:64_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:64_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> 
 ;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">C</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ;<br/>
<b>set </b><font color="Maroon">D</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> ;<br/>
<a NAME="E6:64_1"/>
for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span>  iff <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:64_1_2_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E3:64_1_2_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span>
 ;<br/><a NAME="E4:64_1_2_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">y</font>,<font color="Maroon">w</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:64_1_2_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> 
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:64_1_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font><b> such that </b><br/><a NAME="E4:64_1_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">y</font>,<font color="Maroon">w</font></span>)</span>
 ;<br/>
<a NAME="E5:64_1_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:64_1_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> 
 ;<br/>


</div><b>end;</b></div>
<a NAME="E7:64_1"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Olive">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">z</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : verum </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Olive">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Olive">y</font>,<font color="Maroon">w</font></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b>verum;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font>,   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="lfuzzy_0.html#K8" target="_self">.</a> <font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">w</font></span>)</span>;<br/>
<a NAME="E8:64_1"/><i><font color="Green">E71</font></i>: 
for <font color="Olive">y</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font><br/> for <font color="Olive">z</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">z</font>] holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">y</font>,<font color="Olive">z</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">y</font>,<font color="Olive">z</font>)
 
;<br/>
<a NAME="E9:64_1"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">y</font>,<font color="Olive">z</font>) where <font color="Olive">z</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">z</font>] </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y</font>] </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <span class="p3">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">y1</font>,<font color="Olive">z1</font>) where <font color="Olive">y1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Y</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">y1</font>] </span>}</span> ,<span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p4"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> where <font color="Olive">z1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">Z</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">z1</font>] </span>}</span> ,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span>
 
<b>from </b><i><a class="ref" href="lfuzzy_0.html#S5" target="_self">LFUZZY_0:sch 5</a>(<a class="ref" href="lfuzzy_0.html#D1" target="_self">Def1</a>);<br/></i>
<b>hence </b><a NAME="E10:64_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">x</font>,<font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">x</font>,<font color="Maroon">w</font>
 <b>by </b><i>, , , <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:64"/>
<span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">S</font></span>)</span> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font> <a href="fuzzy_4.html#K3">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="fuzzy_4.html#K3">(#)</a> <font color="Maroon">T</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_3.html#T6">FUNCT_3:6</a></i>;<br/>


</div>
