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<b>let </b><font color="Maroon">S0</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<b>set </b><font color="Maroon">s</font> =  <a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font>;<br/>
<b>set </b><font color="Maroon">ol</font> = the <a href="osalg_1.html#U1" target="_self">Overloading</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font></span>)</span>;<br/>
<a NAME="E1:20"/><i><font color="Green">E24</font></i>: 
( the <a href="osalg_1.html#U1" target="_self">Overloading</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font></span>)</span> <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">S0</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S0</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font></span>)</span> &amp;  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S0</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:20"/>
 <a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font> is <a href="orders_3.html#V1">discrete</a>
 <b>by </b><i><a class="ref" href="orders_3.html#D1">ORDERS_3:def 1</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font></span>)</span>, <font color="Maroon">y</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font></span>)</span>;<br/><b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon">x</font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">y</font>
 ;<br/><a NAME="E2:20_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</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 <span class="p1">(<span class="default"><a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:20_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20"/>
 <a href="osalg_1.html#K2" target="_self">OSSign</a> <font color="Maroon">S0</font> is <a href="osalg_1.html#V6" target="_self">op-discrete</a>
 <b>by </b><i/>;<br/>


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