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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E41">Th53</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: WAYBEL21:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a><br/>  for <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Olive" title="b1">T</font>  st (  for <font color="Olive" title="b3">N</font> being   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Olive" title="b1">T</font>  st  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Olive" title="b3">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">S</font> holds <br/> <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Olive" title="b3">N</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">S</font> ) holds <br/><font color="Olive" title="b2">S</font> is  <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a> </div></div>
