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<b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</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="c2">A</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">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_4.html#K4" title="MSUALG_4:func.4">Class</a> <font color="Maroon" title="c3">R</font></span>)</span> <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">S</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:23_2_2"/><i><font color="Green" title="E10">A11</font></i>: 
for <font color="Olive" title="b1">o</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c4">f</font> <a href="msualg_4.html#K5" title="MSUALG_4:func.5">.</a> <font color="Olive" title="b1">o</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="msualg_4.html#K9" title="MSUALG_4:func.9">QuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Olive" title="b1">o</font>
 <b>and </b><br/><a NAME="E2:23_2_2"/><i><font color="Green" title="E11">A12</font></i>: 
for <font color="Olive" title="b1">o</font> being  <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c5">g</font> <a href="msualg_4.html#K5" title="MSUALG_4:func.5">.</a> <font color="Olive" title="b1">o</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="msualg_4.html#K9" title="MSUALG_4:func.9">QuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Olive" title="b1">o</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:23_2_2_1"/>
<font color="Maroon" title="c6">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="c7">i1</font> = <font color="Maroon" title="c6">i</font> as   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font> ;<br/><a NAME="E3:23_2_2_1"/>
( <font color="Maroon" title="c4">f</font> <a href="msualg_4.html#K5" title="MSUALG_4:func.5">.</a> <font color="Maroon" title="c7">i1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="msualg_4.html#K9" title="MSUALG_4:func.9">QuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c7">i1</font> &amp; <font color="Maroon" title="c5">g</font> <a href="msualg_4.html#K5" title="MSUALG_4:func.5">.</a> <font color="Maroon" title="c7">i1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="msualg_4.html#K9" title="MSUALG_4:func.9">QuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c7">i1</font> )
 <b>by </b><i><a class="txt" href="msualg_4.html#E1:23_2_2"><i><font color="Green" title="E10">A11</font></i></a>, <a class="txt" href="msualg_4.html#E2:23_2_2"><i><font color="Green" title="E11">A12</font></i></a></i>;<br/><b>hence </b><a NAME="E4:23_2_2_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:23_2_2"/>
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>


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