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<b>let </b><font color="Maroon" title="c1">S</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>;<br/>

<b>set </b><font color="Maroon" title="c2">ol</font> = the <a href="osalg_1.html#U1" title="OSALG_1:sel.1">Overloading</a> of <font color="Maroon" title="c1">S</font>;<br/>
<b>assume </b><a NAME="E1:31"/>
<font color="Maroon" title="c1">S</font> is <a href="osalg_1.html#V6" title="OSALG_1:attr.6">op-discrete</a>
 ;<br/>

<a NAME="E2:31"/><b>then </b><i><font color="Green" title="E19">A1</font></i>: 
the <a href="osalg_1.html#U1" title="OSALG_1:sel.1">Overloading</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="osalg_1.html#D5" target="_self" title="OSALG_1:def.5">Def5</a></i>;<br/>
<b>let </b><font color="Maroon" title="c3">o</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D9" target="_self" title="OSALG_1:def.9">OSALG_1:def 9</a><br/><b>let </b><font color="Maroon" title="c4">o2</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D8" target="_self" title="OSALG_1:def.8">OSALG_1:def 8</a><br/>



<b>assume </b><a NAME="E3:31"/>
( <font color="Maroon" title="c3">o</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a> <font color="Maroon" title="c4">o2</font> &amp;  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c3">o</font> <a href="osalg_1.html#R2" title="OSALG_1:pred.2">&lt;=</a>  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c4">o2</font> )
 ;<br/>

<a NAME="E4:31"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c4">o2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="osalg_1.html#U1" title="OSALG_1:sel.1">Overloading</a> of <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="osalg_1.html#D3" target="_self" title="OSALG_1:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E5:31"/>
 <a href="osalg_1.html#K1" title="OSALG_1:func.1">the_result_sort_of</a> <font color="Maroon" title="c3">o</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="osalg_1.html#K1" title="OSALG_1:func.1">the_result_sort_of</a> <font color="Maroon" title="c4">o2</font>
 <b>by </b><i><a class="txt" href="osalg_1.html#E2:31"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="relat_1.html#D10" title="RELAT_1:def.10">RELAT_1:def 10</a></i>;<br/>


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