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

<b>let </b><font color="Maroon">T1</font> be  <a href="msualg_1.html#V4">strict</a> <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">S</font>, <font color="Maroon">T2</font> be  <a href="msualg_1.html#V4">strict</a> <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:78_1_2"/><i><font color="Green">E87</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">T1</font> <a href="pboole.html#R6">=</a>  <a href="osalg_1.html#K5" target="_self">ConstOSSet</a> <font color="Maroon">S</font>,<font color="Maroon">z</font> &amp; ( for <font color="Olive">o</font> being  <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font> holds   <a href="msualg_1.html#K5">Den</a> <font color="Olive">o</font>,<font color="Maroon">T1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3">Args</a> <font color="Olive">o</font>,<font color="Maroon">T1</font></span>)</span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">z1</font> ) )
 ;<br/>

<b>assume </b><a NAME="E2:78_1_2"/><i><font color="Green">E88</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">T2</font> <a href="pboole.html#R6">=</a>  <a href="osalg_1.html#K5" target="_self">ConstOSSet</a> <font color="Maroon">S</font>,<font color="Maroon">z</font> &amp; ( for <font color="Olive">o</font> being  <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font> holds   <a href="msualg_1.html#K5">Den</a> <font color="Olive">o</font>,<font color="Maroon">T2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3">Args</a> <font color="Olive">o</font>,<font color="Maroon">T2</font></span>)</span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">z1</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">o1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:78_1_2_1"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">o1</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>reconsider </b><font color="Maroon">o</font> = <font color="Maroon">o1</font> as   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="osalg_1.html#T3" target="_self">Th3</a></i>;<br/><b>thus </b>the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">T1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o1</font> = 
 <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">T1</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D11">MSUALG_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K3">Args</a> <font color="Maroon">o</font>,<font color="Maroon">T1</font></span>)</span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">z1</font>
<b>by </b><i><a class="ref" href="osalg_1.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="osalg_1.html#K5" target="_self">ConstOSSet</a> <font color="Maroon">S</font>,<font color="Maroon">z</font></span>)</span> <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></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font></span>)</span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">z1</font>
<b>by </b><i><a class="ref" href="osalg_1.html#D4" target="_self">Def4</a>, <a class="ref" href="msualg_1.html#D9">MSUALG_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K3">Args</a> <font color="Maroon">o</font>,<font color="Maroon">T2</font></span>)</span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">z1</font>
<b>by </b><i><a class="ref" href="osalg_1.html#D5" target="_self">Def5</a>, <a class="ref" href="msualg_1.html#D9">MSUALG_1:def 9</a></i>
<br/>.= 
 <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<font color="Maroon">T2</font>
<b>by </b><i><a class="ref" href="osalg_1.html#D5" target="_self">Def5</a></i>
<br/>.= 
the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">T2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o1</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D11">MSUALG_1:def 11</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:78_1_2"/>
<font color="Maroon">T1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T2</font>
 <b>by </b><i><a class="ref" href="osalg_1.html#D4" target="_self">Def4</a>, <a class="ref" href="osalg_1.html#D5" target="_self">Def5</a>, <a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


</div>
