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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: YELLOW_7:41</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="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">S</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">T</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span><br/>  for <font color="Olive" title="b4">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>,<font color="Olive" title="b2">T</font>  st <font color="Olive" title="b3">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">g</font> holds <br/>( ( <font color="Olive" title="b3">f</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  implies <font color="Olive" title="b4">g</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  ) &amp; ( <font color="Olive" title="b4">g</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  implies <font color="Olive" title="b3">f</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  ) &amp; ( <font color="Olive" title="b3">f</font> is  <a href="waybel_0.html#V5" title="WAYBEL_0:attr.5">antitone</a>  implies <font color="Olive" title="b4">g</font> is  <a href="waybel_0.html#V5" title="WAYBEL_0:attr.5">antitone</a>  ) &amp; ( <font color="Olive" title="b4">g</font> is  <a href="waybel_0.html#V5" title="WAYBEL_0:attr.5">antitone</a>  implies <font color="Olive" title="b3">f</font> is  <a href="waybel_0.html#V5" title="WAYBEL_0:attr.5">antitone</a>  ) )</div></div>
