<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: WAYBEL_0:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>   st ( <font color="Olive" title="b1">L</font> is  <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>  or <font color="Olive" title="b1">L</font> is  <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a>  ) holds <br/> for <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b2">X</font> is  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  &amp; <font color="Olive" title="b2">X</font> is  <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a>  &amp; <font color="Olive" title="b3">Y</font> is  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  &amp; <font color="Olive" title="b3">Y</font> is  <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a>  holds <br/><font color="Olive" title="b2">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b3">Y</font> is  <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a> </div></div>
