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<b>let </b><font color="Maroon" title="c1">S0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">s</font> =  <a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font>;<br/>
<b>set </b><font color="Maroon" title="c3">ol</font> = the <a href="osalg_1.html#U1" title="OSALG_1:sel.1">Overloading</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span>;<br/>
<a NAME="E1:20"/><i><font color="Green" title="E12">A1</font></i>: 
( the <a href="osalg_1.html#U1" title="OSALG_1:sel.1">Overloading</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> <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">S0</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="osalg_1.html#D6" target="_self" title="OSALG_1:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E2:20"/>
 <a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font> is <a href="orders_3.html#V1" title="ORDERS_3:attr.1">discrete</a>
 <b>by </b><i><a class="ref" href="orders_3.html#D1" title="ORDERS_3:def.1">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" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span>;<br/><b>assume </b><a NAME="E1:20_1"/>
<font color="Maroon" title="c4">x</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a> <font color="Maroon" title="c5">y</font>
 ;<br/><a NAME="E2:20_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</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 <span class="p1">(<span class="default"><a href="osalg_1.html#K2" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font></span>)</span>
 <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="E3:20_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 <b>by </b><i><a class="txt" href="osalg_1.html#E1:20"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="relat_1.html#D10" title="RELAT_1:def.10">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" title="OSALG_1:func.2">OSSign</a> <font color="Maroon" title="c1">S0</font> is <a href="osalg_1.html#V6" title="OSALG_1:attr.6">op-discrete</a>
 <b>by </b><i><a class="ref" href="osalg_1.html#T3" target="_self" title="OSALG_1:th.3">Th3</a></i>;<br/>


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