<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">f1</font> be    <a href="pboole.html#M3">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font>,<font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font>, <font color="Maroon">f2</font> be    <a href="pboole.html#M3">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font>,<font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:16_1_2"/><i><font color="Green">E28</font></i>: 
( ( for <font color="Olive">o</font> being  <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font> holds  <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">o</font> <a href="hidden.html#R1">=</a> <font color="Olive">o</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">A</font> ) &amp; ( for <font color="Olive">o</font> being  <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font> holds  <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">o</font> <a href="hidden.html#R1">=</a> <font color="Olive">o</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">A</font> ) )
 ;<br/>

<a NAME="E2:16_1_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:16_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">o1</font> = <font color="Maroon">x</font> as   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E3:16_1_2_1"/>
( <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o1</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">A</font> &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o1</font> <a href="msualg_2.html#K3" target="_self">/.</a> <font color="Maroon">A</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:16_1_2_1"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:16_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


</div>
