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<b>let </b><font color="Maroon">C</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">f</font> be    <a href="fuzzy_1.html#M1" target="_self">Membership_Func</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">g</font> be    <a href="fuzzy_1.html#M1" target="_self">Membership_Func</a> of <font color="Maroon">C</font>;<br/>





<b>set </b><font color="Maroon">f1</font> =  <a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">g1</font> =  <a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font>;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fuzzy_1.html#D3" target="_self">FUZZY_1:def 3</a><br/>

 <a href="fuzzy_1.html#K3" target="_self">1_minus</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_1.html#K6" target="_self">\+\</a> <font color="Maroon">g</font></span>)</span> = 
 <a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span>)</span>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<span class="p4">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">g</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p4">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<span class="p4">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">g</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E2:52"/><b>then </b>
<span class="p1">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_1.html#K6" target="_self">\+\</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p4">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<span class="p4">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p4">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">g</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:52"/>
<span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" target="_self">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" target="_self">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">f</font></span>)</span>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K3" target="_self">1_minus</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_1.html#K6" target="_self">\+\</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T25">XXREAL_0:25</a></i>;<br/>


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