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<span class="kw">let </span><font color="Maroon" title="c1">X</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">R</font>, <font color="Olive" title="b2">S</font> being  <a href="fuzzy_2.html#NM1" title="FUZZY_2:NM.1">RMembership_Func</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">R</font> is  <a href="lfuzzy_1.html#V2" title="LFUZZY_1:attr.2">symmetric</a>  &amp; <font color="Olive" title="b2">S</font> is  <a href="lfuzzy_1.html#V2" title="LFUZZY_1:attr.2">symmetric</a>  holds <br/> <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p1">(<span class="default"><a href="lfuzzy_1.html#K1" title="LFUZZY_1:func.1">min</a> <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">S</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="lfuzzy_1.html#K1" title="LFUZZY_1:func.1">min</a> <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font>, <font color="Maroon" title="c3">S</font> be   <a href="fuzzy_2.html#NM1" title="FUZZY_2:NM.1">RMembership_Func</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c1">X</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="c2">R</font> is  <a href="lfuzzy_1.html#V2" title="LFUZZY_1:attr.2">symmetric</a>  &amp; <font color="Maroon" title="c3">S</font> is  <a href="lfuzzy_1.html#V2" title="LFUZZY_1:attr.2">symmetric</a>  implies  <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p1">(<span class="default"><a href="lfuzzy_1.html#K1" title="LFUZZY_1:func.1">min</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="lfuzzy_1.html#K1" title="LFUZZY_1:func.1">min</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:21"/>
( <font color="Maroon" title="c2">R</font> is  <a href="lfuzzy_1.html#V2" title="LFUZZY_1:attr.2">symmetric</a>  &amp; <font color="Maroon" title="c3">S</font> is  <a href="lfuzzy_1.html#V2" title="LFUZZY_1:attr.2">symmetric</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_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p1">(<span class="default"><a href="lfuzzy_1.html#K1" title="LFUZZY_1:func.1">min</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="lfuzzy_1.html#K1" title="LFUZZY_1:func.1">min</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font></span><br/>

<a NAME="E2:21"/><span class="kw">then </span>
(  <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c2">R</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">R</font> &amp;  <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <font color="Maroon" title="c3">S</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">S</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lfuzzy_1.html#D4" target="_self" title="LFUZZY_1:def.4">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:21"/>
 <a href="fuzzy_4.html#K2" title="FUZZY_4:func.2">converse</a> <span class="p1">(<span class="default"><a href="lfuzzy_1.html#K1" title="LFUZZY_1:func.1">min</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="lfuzzy_1.html#K1" title="LFUZZY_1:func.1">min</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fuzzy_4.html#T8" title="FUZZY_4:th.8">FUZZY_4:8</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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