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

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being  <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font>  st <font color="Maroon" title="c1">S</font> is  <a href="osalg_1.html#V8" title="OSALG_1:attr.8">monotone</a>  &amp;  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b1">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">o1</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a> <font color="Olive" title="b2">o2</font> &amp;  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Olive" title="b2">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/><font color="Olive" title="b1">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">o2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">o1</font>, <font color="Maroon" title="c3">o2</font> be   <a href="osalg_1.html#NM2" title="OSALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">S</font> is  <a href="osalg_1.html#V8" title="OSALG_1:attr.8">monotone</a>  &amp;  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c2">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">o1</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a> <font color="Maroon" title="c3">o2</font> &amp;  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c3">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c2">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o2</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:36"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c1">S</font> is  <a href="osalg_1.html#V8" title="OSALG_1:attr.8">monotone</a> 
 <span class="kw">and </span><br/><a NAME="E2:36"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
(  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c2">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">o1</font> <a href="osalg_1.html#R1" title="OSALG_1:pred.1">~=</a> <font color="Maroon" title="c3">o2</font> &amp;  <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c3">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o2</font></span><br/>

<a NAME="E3:36"/>
(  <a href="osalg_1.html#K1" title="OSALG_1:func.1">the_result_sort_of</a> <font color="Maroon" title="c2">o1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="osalg_1.html#K1" title="OSALG_1:func.1">the_result_sort_of</a> <font color="Maroon" title="c3">o2</font> &amp;  <a href="osalg_1.html#K1" title="OSALG_1:func.1">the_result_sort_of</a> <font color="Maroon" title="c3">o2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="osalg_1.html#K1" title="OSALG_1:func.1">the_result_sort_of</a> <font color="Maroon" title="c2">o1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="osalg_1.html#D8" target="_self" title="OSALG_1:def.8">Def8</a></span>;<br/>
<a NAME="E4:36"/><span class="kw">then </span>
 <a href="osalg_1.html#K1" title="OSALG_1:func.1">the_result_sort_of</a> <font color="Maroon" title="c2">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_1.html#K1" title="OSALG_1:func.1">the_result_sort_of</a> <font color="Maroon" title="c3">o2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_2.html#T25" title="ORDERS_2:th.25">ORDERS_2:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:36"/>
<font color="Maroon" title="c2">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="osalg_1.html#D4" target="_self" title="OSALG_1:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
