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

<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>take </b><font color="Maroon" title="c2">g</font> =  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D10" title="WAYBEL_1:def.10">WAYBEL_1:def 10</a><br/>

<b>take </b><font color="Maroon" title="c3">d</font> =  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">L</font>;<br/>

<b>thus </b><a NAME="E1:16"/>
( <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">L</font></span>)</span>,<span class="p2">(<span class="default"><a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">L</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">d</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> &amp; <font color="Maroon" title="c2">g</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> &amp; <font color="Maroon" title="c3">d</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> )
 ;<br/>

<b>let </b><font color="Maroon" title="c4">t</font>, <font color="Maroon" title="c5">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<a NAME="E2:16"/>
( <font color="Maroon" title="c2">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s</font> &amp; <font color="Maroon" title="c3">d</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/>
<b>hence </b><a NAME="E3:16"/>
( (  not <font color="Maroon" title="c4">t</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">s</font> or <font color="Maroon" title="c3">d</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">t</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">s</font> ) &amp; (  not <font color="Maroon" title="c3">d</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">t</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">s</font> or <font color="Maroon" title="c4">t</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">s</font> ) )
 ;<br/>


</div>
