<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">X</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">Q</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <font color="Maroon">X</font></span>)</span>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>





<i><font color="Green">E49</font></i>:  <a href="lfuzzy_0.html#K4">FuzzyLattice</a> <font color="Maroon">X</font> = 
<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1">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">X</font>
<b>by </b><i><a class="ref" href="lfuzzy_0.html#D4">LFUZZY_0:def 4</a></i>
<br/>.= 
 <a href="yellow_1.html#K5">product</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="lfuzzy_0.html#K1">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/>
<a NAME="E2:50"/>
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font> holds  <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p2">(<span class="default"><a href="lfuzzy_0.html#K1">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">a</font> is  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E3:50"/><b>then </b>
<span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">Q</font></span>)</span> <a href="lfuzzy_0.html#K9">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">(<span class="default"><a href="card_3.html#K5">pi</a> <font color="Maroon">Q</font>,<font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="pre_circ.html#K2">--&gt;</a> <span class="p3">(<span class="default"><a href="lfuzzy_0.html#K1">RealPoset</a> <span class="p4"><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">x</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="waybel_3.html#T32">WAYBEL_3:32</a></i>;<br/>
<b>hence </b><a NAME="E4:50"/>
<span class="p1">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">Q</font>,<span class="p2">(<span class="default"><a href="lfuzzy_0.html#K4">FuzzyLattice</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="lfuzzy_0.html#K9">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">(<span class="default"><a href="card_3.html#K5">pi</a> <font color="Maroon">Q</font>,<font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><a href="lfuzzy_0.html#K1">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>
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>


</div>
