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<b>set </b><font color="Maroon">C</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>;<br/>
<b>set </b><font color="Maroon">D</font> = the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>;<br/>
<a NAME="E1:11_1_1"/><i><font color="Green">E46</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S'</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E2:11_1_1"/><i><font color="Green">E50</font></i>: 
the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S'</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:11_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:11_1_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">C</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> as    <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E6:11_1_1"/>
the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E7:11_1_1"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">D</font> = the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> as    <a href="pboole.html#M1">ManySortedSet</a> of the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E9:11_1_1"/><i><font color="Green">E51</font></i>: 
 <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="finseq_2.html#K3">*</a> 
 
;<br/>
<i><font color="Green">E52</font></i>: <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="finseq_2.html#K3">*</a> </span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S'</font> <a href="partfun1.html#K2">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S'</font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
<b>by </b><i><a class="ref" href="relat_1.html#T112">RELAT_1:112</a></i>
;<br/>
<a NAME="E11:11_1_1"/>
 <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
;<br/>
<b>then </b><font color="Maroon">C</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> = 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#NK3" target="_self">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font>
<b>by </b><i/>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S'</font> <a href="partfun1.html#K2">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S'</font></span>)</span> <a href="relat_1.html#K7">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
<b>by </b><i><a class="ref" href="relat_1.html#T112">RELAT_1:112</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">D</font> = <font color="Maroon">D</font> as    <a href="pboole.html#M3">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font>,<font color="Maroon">C</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> <b>by </b><i>, , </i>;<br/>
<b>reconsider </b><font color="Maroon">B</font> =  <a href="msualg_1.html#G3">MSAlgebra</a>(# <font color="Maroon">C</font>,<font color="Maroon">D</font> #) as  <a href="msualg_1.html#V4">strict</a> <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="msualg_1.html#D8">MSUALG_1:def 8</a></i>;<br/>
<b>take </b>
<font color="Maroon">B</font>
;<br/>

<b>thus </b><a NAME="E15:11_1_1"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="relat_1.html#K7">|</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> )
 ;<br/>


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