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<span class="kw">let </span><font color="Maroon" title="c1">C</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="fuzzy_1.html#NM1" title="FUZZY_1:NM.1">Membership_Func</a> of <font color="Maroon" title="c1">C</font> holds   <a href="fuzzy_1.html#K5" title="FUZZY_1:func.5">UMF</a> <font color="Maroon" title="c1">C</font> <a href="fuzzy_1.html#NR2" title="FUZZY_1:NR.2">c=</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="fuzzy_1.html#NM1" title="FUZZY_1:NM.1">Membership_Func</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="fuzzy_1.html#K5" title="FUZZY_1:func.5">UMF</a> <font color="Maroon" title="c1">C</font> <a href="fuzzy_1.html#NR2" title="FUZZY_1:NR.2">c=</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="fuzzy_1.html#D2" target="_self" title="FUZZY_1:def.2">FUZZY_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K5" title="FUZZY_1:func.5">UMF</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">x</font></span><br/>





<a NAME="E1:20"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<a NAME="E2:20"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font> &amp; <span class="p1">(<span class="default"><a href="fuzzy_1.html#K5" title="FUZZY_1:func.5">UMF</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:20"/>
<font color="Maroon" title="c2">f</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K5" title="FUZZY_1:func.5">UMF</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="fuzzy_1.html#T13" target="_self" title="FUZZY_1:th.13">Th14</a></span>; <a class="txt" 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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