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<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being   <a href="algspec1.html#M4" title="ALGSPEC1:mode.4">Algebra</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">E</font> being 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>   st <font color="Olive" title="b1">A</font> is    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Olive" title="b2">E</font> holds <br/><font color="Olive" title="b1">A</font> is    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Olive" title="b2">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font></span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">E</font> being 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>   st <font color="Maroon" title="c2">A</font> is    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Olive" title="b1">E</font> holds <br/><font color="Maroon" title="c2">A</font> is    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Olive" title="b1">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font></span><br/><span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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> implies <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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">T</font> = <font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E1:70"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:70"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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">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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:70"/>
<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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">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/>
<a NAME="E5:70"/><span class="lab"><font color="Green" title="E52">A3</font></span>: 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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">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#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>;<br/>
<a NAME="E6:70"/>
<font color="Maroon" title="c5">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="E7:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A4</font></span>: 
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T59" target="_self" title="ALGSPEC1:th.59">Th59</a></span>;<br/>
<a NAME="E8:70"/>
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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>;<br/>
<a NAME="E9:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A5</font></span>: 
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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:70"><span class="lab"><font color="Green" title="E53">A4</font></span></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">Ss</font> = the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font> as   <a href="pboole.html#NM1" title="PBOOLE:NM.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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> ;<br/>
<a NAME="E11:70"/>
<font color="Maroon" title="c5">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="E12:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A6</font></span>: 
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">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#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T59" target="_self" title="ALGSPEC1:th.59">Th59</a></span>;<br/>
<a NAME="E13:70"/>
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#U4" title="STRUCT_0:sel.4">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#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>;<br/>
<a NAME="E14:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A7</font></span>: 
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:70"><span class="lab"><font color="Green" title="E55">A6</font></span></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>;<br/>
<a NAME="E15:70"/><span class="lab"><font color="Green" title="E57">A8</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> implies the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">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"><span class="p3">(<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#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>)</span>,<span class="p1">(<span class="default"><span class="p2">(<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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:70_1"/><span class="lab"><font color="Green" title="E58">A9</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">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"><span class="p3">(<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#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>)</span>,<span class="p1">(<span class="default"><span class="p2">(<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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>)</span></span><br/><a NAME="E2:70_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A10</font></span>: 
<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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>;<br/><div><span class="lab"><font color="Green" title="E60">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:70_1_1"/><span class="lab"><font color="Green" title="E61">A12</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">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">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">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="p2">(<span class="default">the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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></span>)</span>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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></span>)</span></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">S9</font> = <font color="Maroon" title="c1">S</font> as  non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a> ;<br/><span class="kw">reconsider </span><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">S9</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1_1"><span class="lab"><font color="Green" title="E61">A12</font></span></a></span>;<br/><a NAME="E4:70_1_1"/><span class="lab"><font color="Green" title="E62">A13</font></span>: 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:70"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="txt" href="#E5:70"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>;<br/><a NAME="E5:70_1_1"/>
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E2:70"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>;<br/><span class="kw">hence </span><a NAME="E6:70_1_1"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">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">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">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="p2">(<span class="default">the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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></span>)</span>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default">the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:70_1_1"><span class="lab"><font color="Green" title="E62">A13</font></span></a>, <a class="ref" href="algspec1.html#T60" target="_self" title="ALGSPEC1:th.60">Th60</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:70_1"/><span class="lab"><font color="Green" title="E61">A14</font></span>: 
( not <font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font> implies ( the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#U1" title="MSUALG_1:sel.1">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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E15:70"><span class="lab"><font color="Green" title="E57">A8</font></span></a>, <a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="txt" href="#E5:70"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="txt" href="#E2:70"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>;<br/><a NAME="E5:70_1"/><span class="lab"><font color="Green" title="E62">A15</font></span>: 
<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#U1" title="MSUALG_1:sel.1">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#U1" title="MSUALG_1:sel.1">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:70"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="txt" href="#E1:70_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>;<br/><a NAME="E6:70_1"/><span class="lab"><font color="Green" title="E63">A16</font></span>: 
<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#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>;<br/><a NAME="E7:70_1"/>
<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#U2" title="MSUALG_1:sel.2">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#U2" title="MSUALG_1:sel.2">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:70"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="txt" href="#E1:70_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>;<br/><span class="kw">hence </span><a NAME="E8:70_1"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">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"><span class="p3">(<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#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>)</span>,<span class="p1">(<span class="default"><span class="p2">(<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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:70"><span class="lab"><font color="Green" title="E54">A5</font></span></a>, <a class="txt" href="#E14:70"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="txt" href="#E1:70_1"><span class="lab"><font color="Green" title="E58">A9</font></span></a>, <a class="txt" href="#E5:70_1"><span class="lab"><font color="Green" title="E62">A15</font></span></a>, <a class="txt" href="#E2:70_1"><span class="lab"><font color="Green" title="E59">A10</font></span></a>, <a class="txt" href="#E6:70_1"><span class="lab"><font color="Green" title="E63">A16</font></span></a>, <a class="txt" href="#E3:70_1"><span class="lab"><font color="Green" title="E60">A11</font></span></a>, <a class="txt" href="#E4:70_1"><span class="lab"><font color="Green" title="E61">A14</font></span></a>, <a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">C</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c5">B</font> as    <a href="pboole.html#M2" title="PBOOLE:mode.2">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="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font></span>)</span>,<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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">E</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:70"><span class="lab"><font color="Green" title="E56">A7</font></span></a>, <a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">B9</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="E18:70"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">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#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c5">B</font>
 
;<br/>
<a NAME="E19:70"/><span class="kw">then </span>
<font color="Maroon" title="c5">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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E20:70"/>
<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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
