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<div>:: <span class="kw">deftheorem </span>   defines <a href="poset_1.html#V2" title="POSET_1:attr.2">continuous</a> <a onclick="hs(this)" href="javascript:()">POSET_1:def 4 : <br/></a><span> for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q</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><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">P</font>,<font color="Olive" title="b2">Q</font> holds <br/> ( <font color="Olive" title="b3">f</font> is  <a href="poset_1.html#V2" title="POSET_1:attr.2">continuous</a>  iff ( <font color="Olive" title="b3">f</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  &amp; (  for <font color="Olive" title="b4">L</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="orders_2.html#NM2" title="ORDERS_2:NM.2">Chain</a> of <font color="Olive" title="b1">P</font> holds  <font color="Olive" title="b3">f</font> <a href="waybel_0.html#R4" title="WAYBEL_0:pred.4">preserves_sup_of</a> <font color="Olive" title="b4">L</font> ) ) );<br/></span></div>
