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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">O</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">R</font> be   <a href="orders_1.html#NM2" title="ORDERS_1:NM.2">Order</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c4">Ol</font> be   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon" title="c2">O</font>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c1">A</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/><b>let </b><font color="Maroon" title="c6">g</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c1">A</font>;<br/>











<b>set </b><font color="Maroon" title="c7">RS0</font> =  <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #);<br/>
<a NAME="E1:9"/>
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</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 <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #)
 
<b>by </b><i><a class="ref" href="orders_1.html#T97" title="ORDERS_1:th.97">ORDERS_1:97</a></i>;<br/>
<a NAME="E2:9"/><b>then </b>
( the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) &amp; the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) &amp; the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) <a href="relat_2.html#R4" title="RELAT_2:pred.4">is_antisymmetric_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) )
 
<b>by </b><i><a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a>, <a class="ref" href="relat_2.html#D12" title="RELAT_2:def.12">RELAT_2:def 12</a>, <a class="ref" href="relat_2.html#D16" title="RELAT_2:def.16">RELAT_2:def 16</a></i>;<br/>
<b>hence </b><a NAME="E3:9"/>
( not  <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not  <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> &amp;  <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp;  <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> &amp;  <a href="osalg_1.html#G3" title="OSALG_1:aggr.3">OverloadedRSSign</a>(# <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">O</font>,<font color="Maroon" title="c4">Ol</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font> #) is <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> )
 <b>by </b><i><a class="ref" href="msualg_1.html#D5" title="MSUALG_1:def.5">MSUALG_1:def 5</a>, <a class="ref" href="orders_2.html#D4" title="ORDERS_2:def.4">ORDERS_2:def 4</a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a>, <a class="ref" href="orders_2.html#D6" title="ORDERS_2:def.6">ORDERS_2:def 6</a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>


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