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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="osalg_1.html#L1" target="_self">OverloadedMSSign</a> ;<br/>

<a NAME="E1:15"/>
 <a href="relat_1.html#K3">field</a> the <a href="osalg_1.html#U1" target="_self">Overloading</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T97">ORDERS_1:97</a></i>;<br/>
<a NAME="E2:15"/><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="relat_2.html#R8">is_transitive_in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D16">RELAT_2:def 16</a></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>, <font color="Maroon">o1</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>, <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="E3:15"/>
( <font color="Maroon">o</font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">o1</font> &amp; <font color="Maroon">o1</font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">o2</font> )
 ;<br/>

<a NAME="E4:15"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o1</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> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o1</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/>
<a NAME="E5:15"/><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>, <a class="ref" href="relat_2.html#D8">RELAT_2:def 8</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
<font color="Maroon">o</font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">o2</font>
 <b>by </b><i/>;<br/>


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