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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> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="pralg_2.html#M2" target="_self">MSAlgebra-Family</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="funct_5.html#K4">uncurry</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K12" target="_self">OPER</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<a NAME="E1:31"/>
the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="msualg_1.html#D5">MSUALG_1:def 5</a></i>;<br/>
<a NAME="E2:31"/><b>then </b><i><font color="Green">E14</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T113">ZFMISC_1:113</a></i>;<br/>
<a NAME="E3:31"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K4">uncurry</a> <span class="p2">(<span class="default"><a href="pralg_2.html#K12" target="_self">OPER</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="pralg_2.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E4:31"/><b>then </b>
 <a href="funct_5.html#K4">uncurry</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K12" target="_self">OPER</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="funct_5.html#K4">uncurry</a> <span class="p3">(<span class="default"><a href="pralg_2.html#K12" target="_self">OPER</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<a NAME="E5:31"/><b>then </b>
 <a href="funct_5.html#K5">curry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K4">uncurry</a> <span class="p2">(<span class="default"><a href="pralg_2.html#K12" target="_self">OPER</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><a href="funct_5.html#K4">uncurry</a> <span class="p4">(<span class="default"><a href="pralg_2.html#K12" target="_self">OPER</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="pralg_2.html#E2:31"><i><font color="Green">E14</font></i></a>, <a class="ref" href="funct_6.html#T19">FUNCT_6:19</a></i>;<br/>
<b>hence </b><a NAME="E6:31"/>
 <a href="funct_6.html#K10">commute</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K12" target="_self">OPER</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p3">(<span class="default"><a href="funct_5.html#K4">uncurry</a> <span class="p4">(<span class="default"><a href="pralg_2.html#K12" target="_self">OPER</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/>


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