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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: WAYBEL17:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</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>,<font color="Olive" title="b2">T</font>  st <font color="Olive" title="b3">f</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  holds <br/> for <font color="Olive" title="b4">x</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="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">w</font></span>)</span> where <font color="Olive" title="b5">w</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font> : <font color="Olive" title="b5">w</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Olive" title="b4">x</font> </span> } </span> ,<font color="Olive" title="b2">T</font>)</div></div>
