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<b>let </b><font color="Maroon" title="c1">MS</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="msualg_1.html#V6" title="MSUALG_1:attr.6">segmental</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">MS</font>;<br/><b>let </b><font color="Maroon" title="c3">B</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <a href="msualg_2.html#M1" title="MSUALG_2:mode.1">MSSubAlgebra</a> of <font color="Maroon" title="c2">A</font>;<br/>





<b>reconsider </b><font color="Maroon" title="c4">C</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c3">B</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">A</font> <b>by </b><i><a class="ref" href="msualg_2.html#D10" title="MSUALG_2:def.10">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E2:19"/><i><font color="Green" title="E17">A1</font></i>: 
( <font color="Maroon" title="c4">C</font> is <a href="msualg_2.html#V3" title="MSUALG_2:attr.3">opers_closed</a> &amp; the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c3">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">C</font> )
 
<b>by </b><i><a class="ref" href="msualg_2.html#D10" title="MSUALG_2:def.10">MSUALG_2:def 10</a></i>;<br/>
<a NAME="E3:19"/><i><font color="Green" title="E18">A2</font></i>: 
 <a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1">(<span class="default"><a href="msualg_1.html#K11" title="MSUALG_1:func.11">the_sort_of</a> <font color="Maroon" title="c2">A</font></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_1.html#K12" title="MSUALG_1:func.12">the_charact_of</a> <font color="Maroon" title="c2">A</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msualg_1.html#D19" title="MSUALG_1:def.19">MSUALG_1:def 19</a></i>;<br/>
<a NAME="E4:19"/><i><font color="Green" title="E19">A3</font></i>: 
 <a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1">(<span class="default"><a href="msualg_1.html#K11" title="MSUALG_1:func.11">the_sort_of</a> <font color="Maroon" title="c3">B</font></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_1.html#K12" title="MSUALG_1:func.12">the_charact_of</a> <font color="Maroon" title="c3">B</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msualg_1.html#D19" title="MSUALG_1:def.19">MSUALG_1:def 19</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">S</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font></span>)</span>;<br/>

<b>assume </b><a NAME="E5:19"/><i><font color="Green" title="E20">A4</font></i>: 
<font color="Maroon" title="c5">S</font> <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 <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c3">B</font></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon" title="c6">1B</font> =  <a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c3">B</font>;<br/>
<b>set </b><font color="Maroon" title="c7">1A</font> =  <a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font>;<br/>
<b>set </b><font color="Maroon" title="c8">f1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c3">B</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">f1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c3">B</font></span>)</span> as   <a href="unialg_1.html#NM1" title="UNIALG_1:NM.1">PFuncFinSequence</a> of <font color="Maroon" title="c5">S</font> <b>by </b><i><a class="txt" href="mssublat.html#E5:19"><i><font color="Green" title="E20">A4</font></i></a></i>;<br/>
<a NAME="E7:19"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c9">f1</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="c3">B</font>
 
<b>by </b><i><a class="txt" href="mssublat.html#E4:19"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="msualg_1.html#D18" title="MSUALG_1:def.18">MSUALG_1:def 18</a></i>;<br/>
<b>then </b><i><font color="Green" title="E22">A6</font></i>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c9">f1</font> = 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">MS</font>
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>
<br/>.= 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c2">A</font>
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font></span>)</span>
<b>by </b><i><a class="txt" href="mssublat.html#E3:19"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="msualg_1.html#D18" title="MSUALG_1:def.18">MSUALG_1:def 18</a></i>
;<br/>
<a NAME="E9:19"/>
for <font color="Olive" title="b1">n</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">o</font> being  <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font></span>)</span>  st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c9">f1</font> &amp; <font color="Olive" title="b2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> holds <br/><font color="Maroon" title="c9">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">o</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c5">S</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">n</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c11">o</font> be   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font></span>)</span>;<br/>



<b>assume </b><a NAME="E1:19_2"/><i><font color="Green" title="E23">A7</font></i>: 
( <font color="Maroon" title="c10">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c9">f1</font> &amp; <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">n</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c12">y</font> = <font color="Maroon" title="c10">n</font> as   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">MS</font> <b>by </b><i><a class="txt" href="mssublat.html#E7:19"><i><font color="Green" title="E21">A5</font></i></a>, <a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:19_2"/><i><font color="Green" title="E24">A8</font></i>: 
<font color="Maroon" title="c4">C</font> <a href="msualg_2.html#R1" title="MSUALG_2:pred.1">is_closed_on</a> <font color="Maroon" title="c12">y</font>
 
<b>by </b><i><a class="txt" href="mssublat.html#E2:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="msualg_2.html#D7" title="MSUALG_2:def.7">MSUALG_2:def 7</a></i>;<br/>
<a NAME="E4:19_2"/>
<font color="Maroon" title="c5">S</font> is <a href="unialg_2.html#V1" title="UNIALG_2:attr.1">opers_closed</a>
 
<b>by </b><i><a class="txt" href="mssublat.html#E5:19"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="mssublat.html#T18" target="_self" title="MSSUBLAT:th.18">Th18</a></i>;<br/>
<a NAME="E5:19_2"/><b>then </b><i><font color="Green" title="E25">A9</font></i>: 
<font color="Maroon" title="c5">S</font> <a href="unialg_2.html#R2" title="UNIALG_2:pred.2">is_closed_on</a> <font color="Maroon" title="c11">o</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D5" title="UNIALG_2:def.5">UNIALG_2:def 5</a></i>;<br/>
<a NAME="E6:19_2"/><i><font color="Green" title="E26">A10</font></i>: 
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c12">y</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2_1"><b>proof </b></a><div class="add">

<font color="Maroon" title="c11">o</font> = 
the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">y</font>
<b>by </b><i><a class="txt" href="mssublat.html#E3:19"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="mssublat.html#E1:19_2"><i><font color="Green" title="E23">A7</font></i></a>, <a class="ref" href="msualg_1.html#D18" title="MSUALG_1:def.18">MSUALG_1:def 18</a></i>
<br/>.= 
 <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c2">A</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D11" title="MSUALG_1:def.11">MSUALG_1:def 11</a></i>
;<br/>
<b>then </b><i><font color="Green" title="E27">A11</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c11">o</font> = 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c2">A</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/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c12">y</font></span>)</span></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K11" title="MSUALG_1:func.11">the_sort_of</a> <font color="Maroon" title="c2">A</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#T11" title="MSUALG_1:th.11">MSUALG_1:11</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2_1_3"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon" title="c13">a</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c12">y</font></span>)</span></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K11" title="MSUALG_1:func.11">the_sort_of</a> <font color="Maroon" title="c2">A</font></span>)</span>;<br/><a NAME="E2:19_2_1_3"/>
<font color="Maroon" title="c13">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c11">o</font>
 <b>by </b><i><a class="txt" href="mssublat.html#E2:19_2_1"><i><font color="Green" title="E27">A11</font></i></a></i>;<br/><b>hence </b><a NAME="E3:19_2_1_3"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c11">o</font>
 ;<br/><b>let </b><font color="Maroon" title="c14">x</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/><b>assume </b><a NAME="E4:19_2_1_3"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c11">o</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c15">s</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K11" title="MSUALG_1:func.11">the_sort_of</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> <b> such that </b><br/><a NAME="E6:19_2_1_3"/><i><font color="Green" title="E28">A12</font></i>: 
( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">s</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c12">y</font></span>)</span> )
 <b>by </b><i><a class="txt" href="mssublat.html#E2:19_2_1"><i><font color="Green" title="E27">A11</font></i></a></i>;<br/><b>thus </b><a NAME="E7:19_2_1_3"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c12">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">x</font>
 <b>by </b><i><a class="txt" href="mssublat.html#E6:19_2_1_3"><i><font color="Green" title="E28">A12</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:19_2_1"/>
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c12">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="unialg_1.html#D10" title="UNIALG_1:def.10">UNIALG_1:def 10</a></i>;<br/>


</div><b>end;</b></div>
<i><font color="Green" title="E27">A13</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">C</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 <font color="Maroon" title="c1">MS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">y</font> = 
 <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c3">B</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D9" title="MSUALG_1:def.9">MSUALG_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c11">o</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">S</font>
<b>by </b><i><a class="txt" href="mssublat.html#E4:19"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="mssublat.html#E5:19"><i><font color="Green" title="E20">A4</font></i></a>, <a class="txt" href="mssublat.html#E6:19_2"><i><font color="Green" title="E26">A10</font></i></a>, <a class="ref" href="msualg_1.html#T11" title="MSUALG_1:th.11">MSUALG_1:11</a></i>
;<br/>
<font color="Maroon" title="c9">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">n</font> = 
the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">y</font>
<b>by </b><i><a class="txt" href="mssublat.html#E4:19"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="msualg_1.html#D18" title="MSUALG_1:def.18">MSUALG_1:def 18</a></i>
<br/>.= 
<font color="Maroon" title="c12">y</font> <a href="msualg_2.html#K3" title="MSUALG_2:func.3">/.</a> <font color="Maroon" title="c4">C</font>
<b>by </b><i><a class="txt" href="mssublat.html#E2:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="msualg_2.html#D9" title="MSUALG_2:def.9">MSUALG_2:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">C</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 <font color="Maroon" title="c1">MS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">y</font></span>)</span>
<b>by </b><i><a class="txt" href="mssublat.html#E3:19_2"><i><font color="Green" title="E24">A8</font></i></a>, <a class="ref" href="msualg_2.html#D8" title="MSUALG_2:def.8">MSUALG_2:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">y</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">C</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 <font color="Maroon" title="c1">MS</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">y</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D11" title="MSUALG_1:def.11">MSUALG_1:def 11</a></i>
<br/>.= 
<font color="Maroon" title="c11">o</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c11">o</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c5">S</font></span>)</span>
<b>by </b><i><a class="txt" href="mssublat.html#E3:19"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="mssublat.html#E1:19_2"><i><font color="Green" title="E23">A7</font></i></a>, <a class="txt" href="mssublat.html#E7:19_2"><i><font color="Green" title="E27">A13</font></i></a>, <a class="ref" href="msualg_1.html#D18" title="MSUALG_1:def.18">MSUALG_1:def 18</a></i>
;<br/>
<b>hence </b><a NAME="E9:19_2"/>
<font color="Maroon" title="c9">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o</font> <a href="unialg_2.html#K2" title="UNIALG_2:func.2">/.</a> <font color="Maroon" title="c5">S</font>
 <b>by </b><i><a class="txt" href="mssublat.html#E5:19_2"><i><font color="Green" title="E25">A9</font></i></a>, <a class="ref" href="unialg_2.html#D6" title="UNIALG_2:def.6">UNIALG_2:def 6</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E10:19"/>
the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_2.html#K3" title="UNIALG_2:func.3">Opers</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K13" title="MSUALG_1:func.13">1-Alg</a> <font color="Maroon" title="c2">A</font></span>)</span>,<font color="Maroon" title="c5">S</font>
 <b>by </b><i><a class="txt" href="mssublat.html#E8:19"><i><font color="Green" title="E22">A6</font></i></a>, <a class="ref" href="unialg_2.html#D7" title="UNIALG_2:def.7">UNIALG_2:def 7</a></i>;<br/>


</div>
