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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="fuzzy_1.html#M1">Membership_Func</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green">E3</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="fuzzy_2.html#K1" target="_self">\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green">E4</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fuzzy_2.html#K1" target="_self">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="fuzzy_1.html#D3">FUZZY_1:def 3</a><br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="fuzzy_1.html#D3">FUZZY_1:def 3</a><br/>

<a NAME="E3:19"/>
( <span class="p1">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3">1_minus</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3">1_minus</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="fuzzy_2.html#E1:19"><i><font color="Green">E3</font></i></a>, <a class="txt" href="fuzzy_2.html#E2:19"><i><font color="Green">E4</font></i></a></i>;<br/>
<a NAME="E4:19"/><b>then </b>
 <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3">1_minus</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3">1_minus</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K2">max</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T26">XXREAL_0:26</a></i>;<br/>
<a NAME="E5:19"/><b>then </b>
<span class="p1">(<span class="default"><a href="fuzzy_1.html#K2">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K3">1_minus</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3">1_minus</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="fuzzy_1.html#T6">FUZZY_1:6</a></i>;<br/>
<b>hence </b><a NAME="E6:19"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="fuzzy_1.html#K6">\+\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>


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