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<b>let </b><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</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">g</font> being  <a href="fuzzy_2.html#NM1" title="FUZZY_2:NM.1">RMembership_Func</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font> holds   <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="fuzzy_1.html#K6" title="FUZZY_1:func.6">\+\</a> <font color="Olive" title="b2">g</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="fuzzy_1.html#K6" title="FUZZY_1:func.6">\+\</a> <span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Olive" title="b2">g</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="fuzzy_2.html#NM1" title="FUZZY_2:NM.1">RMembership_Func</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="fuzzy_1.html#K6" title="FUZZY_1:func.6">\+\</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="fuzzy_1.html#K6" title="FUZZY_1:func.6">\+\</a> <span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c4">g</font></span>)</span></span><br/>





 <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="fuzzy_1.html#K6" title="FUZZY_1:func.6">\+\</a> <font color="Maroon" title="c4">g</font></span>)</span> = 
 <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Maroon" title="c3">f</font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c4">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fuzzy_4.html#T7" target="_self" title="FUZZY_4:th.7">Th7</a></i>
<br/>.= 
 <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <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_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c4">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fuzzy_4.html#T8" target="_self" title="FUZZY_4:th.8">Th8</a></i>
<br/>.= 
 <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <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_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span></span>)</span>,<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_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fuzzy_4.html#T8" target="_self" title="FUZZY_4:th.8">Th8</a></i>
<br/>.= 
 <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <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_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <span class="p3">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span></span>)</span>,<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_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fuzzy_4.html#T6" target="_self" title="FUZZY_4:th.6">Th6</a></i>
<br/>.= 
 <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <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_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <span class="p3">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span></span>)</span>,<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> <span class="p3">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fuzzy_4.html#T6" target="_self" title="FUZZY_4:th.6">Th6</a></i>
;<br/>
<b>hence </b><a NAME="E2:15"/>
 <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="fuzzy_1.html#K6" title="FUZZY_1:func.6">\+\</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="fuzzy_1.html#K6" title="FUZZY_1:func.6">\+\</a> <span class="p1">(<span class="default"><a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c4">g</font></span>)</span>
 ; <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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