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<div><span class="kw">theorem </span><a NAME="T55"><span class="comment"><font color="firebrick">:: YELLOW10:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a><br/>  for <font color="Olive" title="b3">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">T</font>  st <font color="Olive" title="b3">X</font> is  <a href="waybel_6.html#V1" title="WAYBEL_6:attr.1">Open</a>  &amp; <font color="Olive" title="b4">Y</font> is  <a href="waybel_6.html#V1" title="WAYBEL_6:attr.1">Open</a>  holds <br/><span class="p1"><a href="yellow_3.html#K6" title="YELLOW_3:func.6">[:</a><span class="default"><font color="Olive" title="b3">X</font>,<font color="Olive" title="b4">Y</font></span><a href="yellow_3.html#K6" title="YELLOW_3:func.6">:]</a></span> is  <a href="waybel_6.html#V1" title="WAYBEL_6:attr.1">Open</a> </div></div>
