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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: WAYBEL34:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</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="b2">k</font> being   <a href="waybel_1.html#V8" title="WAYBEL_1:attr.8">kernel</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">L</font>,<font color="Olive" title="b1">L</font> holds <br/> ( <font color="Olive" title="b2">k</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  iff  <a href="waybel_1.html#K2" title="WAYBEL_1:func.2">corestr</a> <font color="Olive" title="b2">k</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  )</div></div>
