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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">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">Membership_Func</a> of <font color="Maroon">C</font>;<br/>





<a NAME="E1:52"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="yellow_1.html#K5">product</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p3"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#D5">YELLOW_1:def 5</a></i>;<br/>
<b>set </b><font color="Maroon">fg</font> = <span class="p1">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">f</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">g</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">R</font> =  <a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>;<br/>
<b>set </b><font color="Maroon">J</font> = <font color="Maroon">C</font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>;<br/><a NAME="E1:52_1"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font> holds  <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p3"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> <a href="waybel_3.html#K6">.</a> <font color="Olive">c</font> is   <a href="waybel_0.html#NM6">Semilattice</a>
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><a NAME="E2:52_1"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p3"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span></span>)</span></span>)</span> <a href="waybel_3.html#K6">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="lfuzzy_0.html#K1" target="_self">RealPoset</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">0,1</span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="lfuzzy_0.html#K5" target="_self">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">f</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">g</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span></span>)</span></span>)</span> <a href="lfuzzy_0.html#K7" target="_self">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">f</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span> <a href="lfuzzy_0.html#K9" target="_self">.</a> <font color="Maroon">c</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">g</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span> <a href="lfuzzy_0.html#K9" target="_self">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
 <a href="lfuzzy_0.html#K3" target="_self">min</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="lfuzzy_0.html#K7" target="_self">.</a> <font color="Maroon">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="lfuzzy_0.html#K7" target="_self">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<a NAME="E3:52"/><b>then </b>
 <a href="lfuzzy_0.html#K5" target="_self">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">f</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">g</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="fuzzy_1.html#K1">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="fuzzy_1.html#D4">FUZZY_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:52"/>
 <a href="fuzzy_1.html#K1">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">f</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">C</font>,<font color="Maroon">g</font> <a href="lfuzzy_0.html#K6" target="_self">@</a> </span>)</span>
 ;<br/>


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