<?xml version="1.0"?>
<div class="add">

<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>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:88_1"/>
<font color="Maroon" title="c2">X</font> is   <a href="osalg_1.html#NM6" title="OSALG_1:NM.6">OperName</a> of <font color="Maroon" title="c1">S</font>
 ;<br/><a NAME="E2:88_1"/><b>then </b>
<font color="Maroon" title="c2">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="osalg_1.html#K9" title="OSALG_1:func.9">OperNames</a> <font color="Maroon" title="c1">S</font>
 ;<br/><a NAME="E3:88_1"/><b>then </b>
<font color="Maroon" title="c2">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">Class</a> the <a href="osalg_1.html#U1" title="OSALG_1:sel.1">Overloading</a> of <font color="Maroon" title="c1">S</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:88_1"/><i><font color="Green" title="E48">A1</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> the <a href="osalg_1.html#U1" title="OSALG_1:sel.1">Overloading</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">x</font> )
 <b>by </b><i><a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">x1</font> = <font color="Maroon" title="c3">x</font> as   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font> <b>by </b><i><a class="txt" href="osalg_1.html#E5:88_1"><i><font color="Green" title="E48">A1</font></i></a></i>;<br/><b>take </b><font color="Maroon" title="c5">x1</font> = <font color="Maroon" title="c4">x1</font>;<br/><b>thus </b><a NAME="E7:88_1"/>
<font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_1.html#K10" title="OSALG_1:func.10">Name</a> <font color="Maroon" title="c5">x1</font>
 <b>by </b><i><a class="txt" href="osalg_1.html#E5:88_1"><i><font color="Green" title="E48">A1</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon" title="c3">op1</font> being   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font><b> such that </b><a NAME="E2:88"/><i><font color="Green" title="E48">A2</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_1.html#K10" title="OSALG_1:func.10">Name</a> <font color="Maroon" title="c3">op1</font>
 ;<br/>

<a NAME="E3:88"/>
( <font color="Maroon" title="c3">op1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> the <a href="osalg_1.html#U1" title="OSALG_1:sel.1">Overloading</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">op1</font> )
 
<b>by </b><i><a class="txt" href="osalg_1.html#E2:88"><i><font color="Green" title="E48">A2</font></i></a></i>;<br/>
<a NAME="E4:88"/><b>then </b>
<font color="Maroon" title="c2">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K9" title="EQREL_1:func.9">Class</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="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:88"/>
<font color="Maroon" title="c2">X</font> is   <a href="osalg_1.html#NM6" title="OSALG_1:NM.6">OperName</a> of <font color="Maroon" title="c1">S</font>
 ;<br/>


</div>
