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<span class="kw">let </span><font color="Maroon" title="c2">C1</font>, <font color="Maroon" title="c3">C2</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="fuzzy_2.html#NM1" title="FUZZY_2:NM.1">RMembership_Func</a> of <font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font> 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_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>) &amp;  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> (<font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font> &amp;  <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_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font> &amp;  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> (<font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="fuzzy_2.html#NM1" title="FUZZY_2:NM.1">RMembership_Func</a> of <font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> (<font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>) &amp;  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> (<font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> &amp;  <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> (<font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> &amp;  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> (<font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>) )</span><br/>





<a NAME="E1:59"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 <a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzzy_1.html#K5" title="FUZZY_1:func.5">UMF</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
;<br/>
<a NAME="E2:59"/>
 <a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzzy_1.html#K4" title="FUZZY_1:func.4">EMF</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:59"/>
(  <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> (<font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>) &amp;  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> (<font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K5" title="FUZZY_2:func.5">Umf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> &amp;  <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> (<font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f</font> &amp;  <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> (<font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="fuzzy_2.html#K4" title="FUZZY_2:func.4">Zmf</a> (<font color="Maroon" title="c2">C1</font>,<font color="Maroon" title="c3">C2</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:59"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="fuzzy_1.html#T18" onmouseover="rs('fuzzy_1/T18')" onmouseout="rh()">FUZZY_1:18</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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