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<b>let </b><font color="Maroon">C1</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">C2</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">C3</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_3.html#NM1">RMembership_Func</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="fuzzy_3.html#NM1">RMembership_Func</a> of <font color="Maroon">C2</font>,<font color="Maroon">C3</font>, <font color="Maroon">h</font> be   <a href="fuzzy_3.html#NM1">RMembership_Func</a> of <font color="Maroon">C2</font>,<font color="Maroon">C3</font>;<br/><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">C1</font>,<font color="Maroon">C3</font></span><a href="zfmisc_1.html#K2">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="fuzzy_1.html#D3">FUZZY_1:def 3</a><br/>











<b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:21"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C3</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E3:21"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">C1</font>,<font color="Maroon">C3</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:21"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <font color="Maroon">g</font>,<font color="Maroon">h</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><a href="fuzzy_4.html#K2" target="_self">min</a> <font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <font color="Maroon">g</font>,<font color="Maroon">h</font></span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">z</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span> = 
 <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <font color="Maroon">g</font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <font color="Maroon">h</font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="fuzzy_1.html#D4">FUZZY_1:def 4</a></i>
<br/>.= 
 <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <font color="Maroon">g</font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K4">]</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K2">sup</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p3">(<span class="default"><a href="fuzzy_4.html#K2" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">h</font>,<font color="Maroon">x</font>,<font color="Maroon">z</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K2">sup</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p3">(<span class="default"><a href="fuzzy_4.html#K2" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">g</font>,<font color="Maroon">x</font>,<font color="Maroon">z</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K2">sup</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p3">(<span class="default"><a href="fuzzy_4.html#K2" target="_self">min</a> <font color="Maroon">f</font>,<font color="Maroon">h</font>,<font color="Maroon">x</font>,<font color="Maroon">z</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E6:21"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <font color="Maroon">g</font>,<font color="Maroon">h</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K1">min</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="fuzzy_4.html#K3" target="_self">(#)</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font>
 <b>by </b><i>, , </i>;<br/>


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