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<span class="kw">let </span><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <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="c2">A</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="c1">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osalg_4.html#K7" title="OSALG_4:func.7">OSClass</a> <font color="Maroon" title="c3">R</font></span>)</span> <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="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">o</font> being  <a href="osalg_1.html#NM2" title="OSALG_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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="osalg_4.html#K11" title="OSALG_4:func.11">OSQuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Olive" title="b1">o</font> ) &amp; ( for <font color="Olive" title="b1">o</font> being  <a href="osalg_1.html#NM2" title="OSALG_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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="osalg_4.html#K11" title="OSALG_4:func.11">OSQuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Olive" title="b1">o</font> ) implies <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:43_2_2"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
for <font color="Olive" title="b1">o</font> being  <a href="osalg_1.html#NM2" title="OSALG_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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="osalg_4.html#K11" title="OSALG_4:func.11">OSQuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Olive" title="b1">o</font>
 <span class="kw">and </span><br/><a NAME="E2:43_2_2"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
for <font color="Olive" title="b1">o</font> being  <a href="osalg_1.html#NM2" title="OSALG_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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="osalg_4.html#K11" title="OSALG_4:func.11">OSQuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Olive" title="b1">o</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="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_2_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">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="c6">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 <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> )</span><br/><span class="kw">assume </span><a NAME="E1:43_2_2_1"/>
<font color="Maroon" title="c6">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"> <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></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">i1</font> = <font color="Maroon" title="c6">i</font> as   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font> ;<br/><a NAME="E3:43_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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="osalg_4.html#K11" title="OSALG_4:func.11">OSQuotArgs</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c7">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43_2_2"><span class="lab"><font color="Green" title="E21">A7</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:43_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43_2_2"><span class="lab"><font color="Green" title="E22">A8</font></span></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">hence </span><a NAME="E4:43_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</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/>


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