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

<span class="kw">let </span><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be   <a href="fuzimpl3.html#NM1" title="FUZIMPL3:NM.1">Fuzzy_Negation</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">A</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">fg</font> =  <a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c5">mfg</font> = <span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>);<br/>
<a NAME="E1:82"/><span class="lab"><font color="Green" title="E40">B1</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:82"/><span class="lab"><font color="Green" title="E41">AC</font></span>: 
( <font color="Maroon" title="c1">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>) &amp; <font color="Maroon" title="c2">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>) &amp;  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="fuzimpl4.html#E51"><span class="lab"><font color="Green" title="E33">LemmaFunc2</font></span></a></span>;<br/>
<a NAME="E3:82"/>
<span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:82"><span class="lab"><font color="Green" title="E41">AC</font></span></a>, <a class="ref" href="binop_1.html#T17" onmouseover="rs('binop_1/T17')" onmouseout="rh()">BINOP_1:17</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">f1</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E5:82"/><span class="lab"><font color="Green" title="E42">C1</font></span>: 
( <span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f1</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c6">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c6">f1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" onmouseover="rs('funct_2/D2')" onmouseout="rh()">FUNCT_2:def 2</a></span>;<br/>
<a NAME="E6:82"/>
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> holds <br/><span class="p1">(<span class="default"><a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="82_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> implies <span class="p1">(<span class="default"><a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:82_1"/><span class="lab"><font color="Green" title="E43">D0</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c8">f2</font>, <font color="Maroon" title="c9">g2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><span class="kw"> such that </span><br/><a NAME="E3:82_1"/><span class="lab"><font color="Green" title="E44">D1</font></span>: 
( <font color="Maroon" title="c8">f2</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c1">f</font> &amp; <font color="Maroon" title="c9">g2</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c2">g</font> &amp;  <a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>) <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="cousin2.html#K2" title="COUSIN2:func.2">max</a> (<font color="Maroon" title="c8">f2</font>,<font color="Maroon" title="c9">g2</font>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzimpl4.html#D9" target="_self" onmouseover="rs('fuzimpl4/D9')" onmouseout="rh()">MaxFuz</a></span>;<br/>
<a NAME="E4:82_1"/>
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a>, <a class="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">fA</font> = <font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c11">gA</font> = <font color="Maroon" title="c2">g</font> as    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>) <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" onmouseover="rs('funct_2/D2')" onmouseout="rh()">FUNCT_2:def 2</a></span>;<br/>
<a NAME="E6:82_1"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> (<font color="Maroon" title="c10">fA</font>,<font color="Maroon" title="c11">gA</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> (<font color="Maroon" title="c10">fA</font>,<font color="Maroon" title="c11">gA</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<a href="real_lat.html#K2" title="REAL_LAT:func.2">maxreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c10">fA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">gA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:82_1"><span class="lab"><font color="Green" title="E43">D0</font></span></a>, <a class="ref" href="funcop_1.html#T22" onmouseover="rs('funcop_1/T22')" onmouseout="rh()">FUNCOP_1:22</a></span>
<br/>.= 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c10">fA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">gA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#D2" onmouseover="rs('real_lat/D2')" onmouseout="rh()">REAL_LAT:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:82_1"><span class="lab"><font color="Green" title="E44">D1</font></span></a>, <a class="txt" href="#E1:82_1"><span class="lab"><font color="Green" title="E43">D0</font></span></a>, <a class="ref" href="cousin2.html#D2" onmouseover="rs('cousin2/D2')" onmouseout="rh()">COUSIN2:def 2</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:82_1"/>
<span class="p1">(<span class="default"><a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="real_lat.html#D4" onmouseover="rs('real_lat/D4')" onmouseout="rh()">REAL_LAT:def 4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:82"/>
 <a href="fuzimpl4.html#K3" title="FUZIMPL4:func.3">max</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_lat.html#K4" title="REAL_LAT:func.4">maxfuncreal</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:82"><span class="lab"><font color="Green" title="E42">C1</font></span></a>, <a class="txt" href="#E1:82"><span class="lab"><font color="Green" title="E40">B1</font></span></a>, <a class="ref" href="funct_1.html#T2" onmouseover="rs('funct_1/T2')" onmouseout="rh()">FUNCT_1:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
