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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E44">Th41</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: WAYBEL27:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font>, <font color="Olive" title="b3">T</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>  ex <font color="Olive" title="b4">F</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> (<font color="Olive" title="b2">S</font>,<span class="p2">(<span class="default"><font color="Olive" title="b3">T</font> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a> <font color="Olive" title="b1">X</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> (<font color="Olive" title="b2">S</font>,<font color="Olive" title="b3">T</font>)</span>)</span> <a href="yellow_1.html#K5" title="YELLOW_1:func.5">|^</a> <font color="Olive" title="b1">X</font></span>)</span> st <br/>( <font color="Olive" title="b4">F</font> is  <a href="waybel27.html#V3" title="WAYBEL27:attr.3">commuting</a>  &amp; <font color="Olive" title="b4">F</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>  )</div></div>
