<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T33"><span class="comment"><font color="firebrick">:: WAYBEL_5:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>  st <font color="Olive" title="b1">L</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  holds <br/> for <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>  st  ex <font color="Olive" title="b3">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">L</font>,<font color="Olive" title="b2">S</font> st <br/>( <font color="Olive" title="b3">g</font> is  <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>  &amp; <font color="Olive" title="b3">g</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  &amp; <font color="Olive" title="b3">g</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  ) holds <br/><font color="Olive" title="b2">S</font> is   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a></div></div>
