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

<b>let </b><font color="Maroon">L</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:48"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> &amp;  <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <font color="Maroon">X</font>,<font color="Maroon">L</font> &amp;  <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <font color="Maroon">Y</font>,<font color="Maroon">L</font> )
 ;<br/>

<a NAME="E2:48"/>
 <a href="yellow_0.html#K2" target="_self">"/\"</a> <font color="Maroon">Y</font>,<font color="Maroon">L</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a><br/>

<b>assume </b><a NAME="E1:48_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:48_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp;  <a href="yellow_0.html#K2" target="_self">"/\"</a> <font color="Maroon">Y</font>,<font color="Maroon">L</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">Y</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:48_1"/>
 <a href="yellow_0.html#K2" target="_self">"/\"</a> <font color="Maroon">Y</font>,<font color="Maroon">L</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:48"/>
 <a href="yellow_0.html#K2" target="_self">"/\"</a> <font color="Maroon">X</font>,<font color="Maroon">L</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="yellow_0.html#K2" target="_self">"/\"</a> <font color="Maroon">Y</font>,<font color="Maroon">L</font>
 <b>by </b><i>, </i>;<br/>


</div>
