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<b>let </b><font color="Maroon">S</font> be   <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">o1</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">o2</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">o3</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:71"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">o1</font> <a href="osalg_1.html#R6" target="_self">&lt;=</a> <font color="Maroon">o2</font> &amp; <font color="Maroon">o2</font> <a href="osalg_1.html#R6" target="_self">&lt;=</a> <font color="Maroon">o3</font> )
 ;<br/>

<a NAME="E2:71"/><b>then </b><i><font color="Green">E40</font></i>: 
( <font color="Maroon">o1</font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">o2</font> &amp;  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o1</font> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o2</font> &amp;  <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o1</font> <a href="orders_2.html#R3">&lt;=</a>  <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o2</font> )
 
<b>by </b><i><a class="ref" href="osalg_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E3:71"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">o2</font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">o3</font> &amp;  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o2</font> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o3</font> &amp;  <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o2</font> <a href="orders_2.html#R3">&lt;=</a>  <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o3</font> )
 
<b>by </b><i><a class="txt" href="osalg_1.html#E2:71"><i><font color="Green">E40</font></i></a>, <a class="ref" href="osalg_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E4:71"/>
<font color="Maroon">o1</font> <a href="osalg_1.html#R1" target="_self">~=</a> <font color="Maroon">o3</font>
 <b>by </b><i><a class="ref" href="osalg_1.html#T2" target="_self">Th2</a>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="osalg_1.html#D22" target="_self">OSALG_1:def 22</a><br/>

<b>thus </b><a NAME="E5:71"/>
 <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o1</font> <a href="osalg_1.html#R2" target="_self">&lt;=</a>  <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o3</font>
 <b>by </b><i><a class="ref" href="osalg_1.html#T2" target="_self">Th2</a>, , </i>;<br/>

<b>thus </b><a NAME="E6:71"/>
 <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o1</font> <a href="orders_2.html#R3">&lt;=</a>  <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o3</font>
 <b>by </b><i><a class="ref" href="osalg_1.html#T2" target="_self">Th2</a>, , <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/>


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