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<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>, <font color="Olive" title="b3">h</font> being  <a href="fuzzy_1.html#NM1" title="FUZZY_1:NM.1">Membership_Func</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Olive" title="b2">g</font></span>)</span> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Olive" title="b3">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Olive" title="b2">g</font>,<font color="Olive" title="b3">h</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font>, <font color="Maroon" title="c4">h</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Maroon" title="c4">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span>)</span></span><br/>







<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Maroon" title="c4">h</font> = 
 <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</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> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c3">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzzy_1.html#T8" title="FUZZY_1:th.8">FUZZY_1:8</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fuzzy_1.html#T12" title="FUZZY_1:th.12">FUZZY_1:12</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/>


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