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

<span class="kw">let </span><font color="Maroon" title="c1">C</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="fuzzy_1.html#NM1" title="FUZZY_1:NM.1">Membership_Func</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">g</font> <a href="fuzzy_1.html#NR2" title="FUZZY_1:NR.2">c=</a>  holds <br/> <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">g</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be   <a href="fuzzy_1.html#NM1" title="FUZZY_1:NM.1">Membership_Func</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">g</font> <a href="fuzzy_1.html#NR2" title="FUZZY_1:NR.2">c=</a>  implies  <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">g</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:28"/>
<font color="Maroon" title="c3">g</font> <a href="fuzzy_1.html#NR2" title="FUZZY_1:NR.2">c=</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">g</font></span><br/>

<a NAME="E2:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon" title="c3">g</font> <a href="fuzzy_1.html#NR2" title="FUZZY_1:NR.2">c=</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzzy_1.html#T20" target="_self" title="FUZZY_1:th.20">Th20</a></span>;<br/>
<a NAME="E3:28"/>
 <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font> <a href="fuzzy_1.html#NR2" title="FUZZY_1:NR.2">c=</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzzy_1.html#T18" target="_self" title="FUZZY_1:th.18">Th18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:28"/>
 <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="fuzzy_1.html#E6"><span class="lab"><font color="Green" title="E3">Lm1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
