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<b>let </b><font color="Maroon">S</font> be   <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">S</font>;<br/>



<b>assume </b><a NAME="E1:77"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">S</font> is <a href="orders_3.html#V1">discrete</a> or <font color="Maroon">S</font> is <a href="osalg_1.html#V6" target="_self">op-discrete</a> )
 ;<br/>

<b>let </b><font color="Maroon">o1</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D23" target="_self">OSALG_1:def 23</a><br/><b>let </b><font color="Maroon">o2</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/>



<b>assume </b><a NAME="E2:77"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">o1</font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">o2</font> &amp;  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o1</font> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o2</font> &amp;  <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o1</font> <a href="orders_2.html#R3">&lt;=</a>  <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o2</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D22" target="_self">OSALG_1:def 22</a><br/>

<a NAME="E3:77"/>
<font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:77_1_1"/>
( <font color="Maroon">S</font> is <a href="orders_3.html#V1">discrete</a> or <font color="Maroon">S</font> is <a href="osalg_1.html#V6" target="_self">op-discrete</a> )
 </span><b>by </b><i><a class="ref" href="osalg_1.html#D4" target="_self">Def4</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_1_1"><b>suppose </b></a><a NAME="E1:77_1_1_1"/>
<font color="Maroon">S</font> is <a href="orders_3.html#V1">discrete</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:77_1_1_1"/>
<font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o2</font>
 <b>by </b><i><a class="ref" href="osalg_1.html#D5" target="_self">Def5</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_1_2"><b>suppose </b></a><a NAME="E1:77_1_1_2"/>
<font color="Maroon">S</font> is <a href="osalg_1.html#V6" target="_self">op-discrete</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:77_1_1_2"/>
<font color="Maroon">o1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o2</font>
 <b>by </b><i><a class="ref" href="osalg_1.html#D5" target="_self">Def5</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E4:77"/>
<span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o2</font>,<font color="Maroon">A</font></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K3">Args</a> <font color="Maroon">o1</font>,<font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o1</font>,<font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T40">FUNCT_2:40</a></i>;<br/>


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