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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be    <a href="algspec1.html#M4" title="ALGSPEC1:mode.4">Algebra</a> of <font color="Maroon" title="c1">S</font>;<br/><b>let </b><font color="Maroon" title="c3">E</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/>





<b>assume </b><a NAME="E1:70"/>
<font color="Maroon" title="c2">A</font> is    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c3">E</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">B</font> = <font color="Maroon" title="c2">A</font> as    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c3">E</font> ;<br/>
<b>set </b><font color="Maroon" title="c5">T</font> = <font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E3:70"/><i><font color="Green" title="E51">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">E</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E4:70"/>
<font color="Maroon" title="c4">B</font> is    <a href="algspec1.html#M4" title="ALGSPEC1:mode.4">Algebra</a> of <font color="Maroon" title="c1">S</font>
 
;<br/>
<a NAME="E5:70"/><b>then </b><i><font color="Green" title="E52">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">E</font>
 
<b>by </b><i><a class="ref" href="algspec1.html#T59" target="_self" title="ALGSPEC1:th.59">Th59</a></i>;<br/>
<a NAME="E6:70"/><b>then </b><i><font color="Green" title="E53">A3</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">E</font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E3:70"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">Ss</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">B</font> as    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <b>by </b><i><a class="txt" href="algspec1.html#E3:70"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="algspec1.html#E5:70"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E8:70"/><i><font color="Green" title="E54">A4</font></i>: 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c3">E</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E9:70"/>
<font color="Maroon" title="c4">B</font> is    <a href="algspec1.html#M4" title="ALGSPEC1:mode.4">Algebra</a> of <font color="Maroon" title="c1">S</font>
 
;<br/>
<a NAME="E10:70"/><b>then </b>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c3">E</font>
 
<b>by </b><i><a class="ref" href="algspec1.html#T59" target="_self" title="ALGSPEC1:th.59">Th59</a></i>;<br/>
<a NAME="E11:70"/><b>then </b><i><font color="Green" title="E55">A5</font></i>: 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c3">E</font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E8:70"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E12:70"/><i><font color="Green" title="E56">A6</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E13:70"/><i><font color="Green" title="E57">A7</font></i>: 
( the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c3">E</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c1">S</font> &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c3">E</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c1">S</font> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:70_1"/><i><font color="Green" title="E58">A8</font></i>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span>
 ;<br/><a NAME="E2:70_1"/><b>then </b><i><font color="Green" title="E59">A9</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c3">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Ss</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c3">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c3">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c3">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> )
 <b>by </b><i><a class="txt" href="algspec1.html#E11:70"><i><font color="Green" title="E55">A5</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>;<br/><a NAME="E3:70_1"/><i><font color="Green" title="E60">A10</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Ss</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span> )
 <b>by </b><i><a class="txt" href="algspec1.html#E1:70_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>;<br/><div><i><font color="Green" title="E61">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:70_1_1"/><i><font color="Green" title="E62">A12</font></i>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c8">S'</font> = <font color="Maroon" title="c1">S</font> as  non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a> <b>by </b><i><a class="ref" href="msualg_1.html#D5" title="MSUALG_1:def.5">MSUALG_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">o</font> = <font color="Maroon" title="c7">i</font> as   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c8">S'</font> <b>by </b><i><a class="txt" href="algspec1.html#E1:70_1_1"><i><font color="Green" title="E62">A12</font></i></a></i>;<br/><a NAME="E4:70_1_1"/>
( <font color="Maroon" title="c4">B</font> is    <a href="algspec1.html#M4" title="ALGSPEC1:mode.4">Algebra</a> of <font color="Maroon" title="c8">S'</font> &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K2" title="MSUALG_1:func.2">the_result_sort_of</a> <font color="Maroon" title="c9">o</font> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c9">o</font> )
 <b>by </b><i><a class="txt" href="algspec1.html#E12:70"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="algspec1.html#E13:70"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>;<br/><b>hence </b><a NAME="E5:70_1_1"/>
the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default">the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">B</font> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="algspec1.html#T60" target="_self" title="ALGSPEC1:th.60">Th60</a></i>;<br/></div><b>end;</b></div><a NAME="E5:70_1"/>
( not <font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font> implies ( the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <font color="Maroon" title="c3">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> &amp; the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <font color="Maroon" title="c3">E</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> ) )
 <b>by </b><i><a class="txt" href="algspec1.html#E12:70"><i><font color="Green" title="E56">A6</font></i></a>, <a class="txt" href="algspec1.html#E13:70"><i><font color="Green" title="E57">A7</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>;<br/><b>hence </b><a NAME="E6:70_1"/>
the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
 <b>by </b><i><a class="txt" href="algspec1.html#E6:70"><i><font color="Green" title="E53">A3</font></i></a>, <a class="txt" href="algspec1.html#E11:70"><i><font color="Green" title="E55">A5</font></i></a>, <a class="txt" href="algspec1.html#E1:70_1"><i><font color="Green" title="E58">A8</font></i></a>, <a class="txt" href="algspec1.html#E2:70_1"><i><font color="Green" title="E59">A9</font></i></a>, <a class="txt" href="algspec1.html#E3:70_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="txt" href="algspec1.html#E4:70_1"><i><font color="Green" title="E61">A11</font></i></a>, <a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c7">C</font> = the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c4">B</font> as    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K6" title="PBOOLE:func.6">#</a> </span>)</span> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span>,<font color="Maroon" title="c6">Ss</font> <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <b>by </b><i><a class="txt" href="algspec1.html#E11:70"><i><font color="Green" title="E55">A5</font></i></a>, <a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">B'</font> =  <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# <font color="Maroon" title="c6">Ss</font>,<font color="Maroon" title="c7">C</font> #);<br/>
<a NAME="E16:70"/>
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# <font color="Maroon" title="c6">Ss</font>,<font color="Maroon" title="c7">C</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c4">B</font> &amp; the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <a href="msualg_1.html#G3" title="MSUALG_1:aggr.3">MSAlgebra</a>(# <font color="Maroon" title="c6">Ss</font>,<font color="Maroon" title="c7">C</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c4">B</font> )
 
;<br/>
<a NAME="E17:70"/><b>then </b>
<font color="Maroon" title="c4">B</font> is    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font>
 
;<br/>
<b>hence </b><a NAME="E18:70"/>
<font color="Maroon" title="c2">A</font> is    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c3">E</font> <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon" title="c1">S</font>
 ;<br/>


</div>
