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

<b>let </b><font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">t</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:16_1_2"/><i><font color="Green" title="E11">A12</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">s</font>
 <b>and </b><br/><a NAME="E2:16_1_2"/><i><font color="Green" title="E12">A13</font></i>: 
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>and </b><br/><a NAME="E3:16_1_2"/><i><font color="Green" title="E13">A14</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">t</font>
 <b>and </b><br/><a NAME="E4:16_1_2"/><i><font color="Green" title="E14">A15</font></i>: 
<font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c5">A</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="orders_2.html#NM2" title="ORDERS_2:NM.2">Chain</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E6:16_1_2"/><i><font color="Green" title="E15">A16</font></i>: 
( ( for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> holds <br/><font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">s</font> ) &amp; <font color="Maroon" title="c3">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> )
 <b>and </b><br/><a NAME="E7:16_1_2"/><i><font color="Green" title="E16">A17</font></i>: 
( ( for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> holds <br/><font color="Olive" title="b1">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">t</font> ) &amp; <font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">A</font> )
 <b>by </b><i><a class="txt" href="lattice7.html#E1:16_1_2"><i><font color="Green" title="E11">A12</font></i></a>, <a class="txt" href="lattice7.html#E2:16_1_2"><i><font color="Green" title="E12">A13</font></i></a>, <a class="txt" href="lattice7.html#E3:16_1_2"><i><font color="Green" title="E13">A14</font></i></a>, <a class="txt" href="lattice7.html#E4:16_1_2"><i><font color="Green" title="E14">A15</font></i></a></i>;<br/>
<a NAME="E8:16_1_2"/><i><font color="Green" title="E17">A18</font></i>: 
<font color="Maroon" title="c4">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">s</font>
 
<b>by </b><i><a class="txt" href="lattice7.html#E6:16_1_2"><i><font color="Green" title="E15">A16</font></i></a>, <a class="txt" href="lattice7.html#E7:16_1_2"><i><font color="Green" title="E16">A17</font></i></a></i>;<br/>
<a NAME="E9:16_1_2"/>
<font color="Maroon" title="c3">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">t</font>
 
<b>by </b><i><a class="txt" href="lattice7.html#E6:16_1_2"><i><font color="Green" title="E15">A16</font></i></a>, <a class="txt" href="lattice7.html#E7:16_1_2"><i><font color="Green" title="E16">A17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:16_1_2"/>
<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t</font>
 <b>by </b><i><a class="txt" href="lattice7.html#E8:16_1_2"><i><font color="Green" title="E17">A18</font></i></a>, <a class="ref" href="orders_2.html#T25" title="ORDERS_2:th.25">ORDERS_2:25</a></i>;<br/>


</div>
