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

<b>set </b><font color="Maroon">ol</font> = the <a href="osalg_1.html#U1" target="_self">Overloading</a> of <font color="Maroon">S</font>;<br/>
<b>assume </b><a NAME="E1:31"/>
<font color="Maroon">S</font> is <a href="osalg_1.html#V6" target="_self">op-discrete</a>
 ;<br/>

<a NAME="E2:31"/><b>then </b><i><font color="Green">E24</font></i>: 
the <a href="osalg_1.html#U1" target="_self">Overloading</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">o</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#D9" target="_self">OSALG_1:def 9</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>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D8" target="_self">OSALG_1:def 8</a><br/>



<b>assume </b><a NAME="E3:31"/>
( <font color="Maroon">o</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">o</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> )
 ;<br/>

<a NAME="E4:31"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="osalg_1.html#U1" target="_self">Overloading</a> of <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:31"/>
 <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o</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>
 <b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>


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