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

<b>let </b><font color="Maroon" title="c2">M</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>

<b>assume </b><a NAME="E1:24_2_1"/><i><font color="Green" title="E17">A5</font></i>: 
( not <font color="Maroon" title="c2">M</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">M</font> is <a href="yellow11.html#V2" title="YELLOW11:attr.2">interval</a> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E3:24_2_1"/><i><font color="Green" title="E18">A6</font></i>: 
<font color="Maroon" title="c2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="yellow11.html#K3" title="YELLOW11:func.3">[#</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font></span><a href="yellow11.html#K3" title="YELLOW11:func.3">#]</a></span>
 <b>by </b><i><a class="ref" href="yellow11.html#D5" target="_self" title="YELLOW11:def.5">Def5</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D2" title="WAYBEL_0:def.2">WAYBEL_0:def 2</a><br/>

<b>assume </b><a NAME="E4:24_2_1"/><i><font color="Green" title="E19">A7</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font> )
 ;<br/>

<b>take </b>
<font color="Maroon" title="c3">a</font>
;<br/>

<b>consider </b><font color="Maroon" title="c7">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:24_2_1"/><i><font color="Green" title="E20">A8</font></i>: 
<font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:24_2_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">z</font> = <font color="Maroon" title="c7">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E6:24_2_1"><i><font color="Green" title="E20">A8</font></i></a></i>;<br/>
<a NAME="E8:24_2_1"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">z</font> &amp; <font color="Maroon" title="c8">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E3:24_2_1"><i><font color="Green" title="E18">A6</font></i></a>, <a class="txt" href="yellow11.html#E6:24_2_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>
<a NAME="E9:24_2_1"/><b>then </b>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/>
<b>hence </b><a NAME="E10:24_2_1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E3:24_2_1"><i><font color="Green" title="E18">A6</font></i></a>, <a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>

<b>thus </b><a NAME="E11:24_2_1"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">y</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E3:24_2_1"><i><font color="Green" title="E18">A6</font></i></a>, <a class="txt" href="yellow11.html#E4:24_2_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="yellow11.html#D4" target="_self" title="YELLOW11:def.4">Def4</a></i>;<br/>


</div>
