<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T55"><span class="comment"><font color="firebrick">:: WAYBEL_0:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a><br/>  for <font color="Olive" title="b2">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font>  st (  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Olive" title="b2">X</font>,<font color="Olive" title="b1">L</font> or <font color="Olive" title="b1">L</font> is  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  ) holds <br/> <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Olive" title="b2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K11" title="WAYBEL_0:func.11">finsups</a> <font color="Olive" title="b2">X</font></span>)</span></div></div>
