<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th23</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: WAYBEL27:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</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> <br/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font>)</span>)</span> holds <br/> ( <font color="Olive" title="b3">f</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b4">g</font> iff  for <font color="Olive" title="b5">s</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font> holds  <font color="Olive" title="b3">f</font> <a href="waybel27.html#K3" title="WAYBEL27:func.3">.</a> <font color="Olive" title="b5">s</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b4">g</font> <a href="waybel27.html#K3" title="WAYBEL27:func.3">.</a> <font color="Olive" title="b5">s</font> )</div></div>
