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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th28</font></span>: <a NAME="T28"><span class="comment"><font color="firebrick">:: WAYBEL34:28</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="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><br/>  for <font color="Olive" title="b3">g</font> being   <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>  <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">g</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">V7</a>() holds <br/> for <font color="Olive" title="b4">X</font> being   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Olive" title="b2">T</font><br/>  for <font color="Olive" title="b5">Y</font> being   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b6">d</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b4">X</font>,<font color="Olive" title="b5">Y</font>  st <font color="Olive" title="b6">d</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Olive" title="b3">g</font> holds <br/>( <font color="Olive" title="b3">g</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  iff <font color="Olive" title="b6">d</font> is  <a href="t_0topsp.html#V1" title="T_0TOPSP:attr.1">open</a>  )</div></div>
