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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">h</font>, <font color="Olive" title="b3">g</font> being   <a href="fuzzy_1.html#M1" title="FUZZY_1:mode.1">Membership_Func</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b2">h</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>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Olive" title="b3">g</font>,<font color="Olive" title="b2">h</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">g</font></span>)</span>,<font color="Olive" title="b2">h</font></span><br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">h</font>, <font color="Maroon" title="c4">g</font> be    <a href="fuzzy_1.html#M1" title="FUZZY_1:mode.1">Membership_Func</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">h</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>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c3">h</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c3">h</font> )</span><br/>







<b>assume </b><a NAME="E1:2"/><i><font color="Green" title="E2">A1</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="fuzzy_1.html#NR2" title="FUZZY_1:NR.2">c=</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c3">h</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c3">h</font></span><br/>

<b>thus </b> <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Maroon" title="c4">g</font>,<font color="Maroon" title="c3">h</font></span>)</span> = 
 <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<span class="p1">(<span class="default"><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">h</font></span>)</span>
<b>by </b><i><a class="ref" href="fuzzy_1.html#T10" title="FUZZY_1:th.10">FUZZY_1:10</a></i>
<br/>.= 
 <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c4">g</font></span>)</span>,<font color="Maroon" title="c3">h</font>
<b>by </b><i><a class="txt" href="#E1:2"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="fuzzy_1.html#T23" title="FUZZY_1:th.23">FUZZY_1:23</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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