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





<b>set </b><font color="Maroon">A</font> = <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">B</font> = <font color="Maroon">g</font>;<br/>
<b>assume </b><a NAME="E1:8"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">g</font> <a href="fuzzy_1.html#NR2" target="_self">c=</a>  &amp; <font color="Maroon">f</font> <a href="fuzzy_1.html#NR2" target="_self">c=</a>  )
 ;<br/>

<a NAME="E2:8"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:8"/>
for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>  st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> holds <br/><font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </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="E1:8_1"/>
( <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">g</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> &amp; <font color="Maroon">g</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:8_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> implies <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:8"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i>, <a class="ref" href="partfun1.html#T34">PARTFUN1:34</a></i>;<br/>


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