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

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="waybel_0.html#V24">up-complete</a> <a href="waybel11.html#V4" target="_self">Scott</a>  <a href="waybel_9.html#L1">TopRelStr</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>;<br/>



<a NAME="E1:32"/>
(  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">x</font> is <a href="waybel11.html#V2" target="_self">closed_under_directed_sups</a> &amp;  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">x</font> is <a href="waybel_0.html#V12">lower</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:32"/>
 <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">x</font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i/>;<br/>


</div>
