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<div><span class="kw">theorem </span><a NAME="T5"><span class="comment"><font color="firebrick">:: WAYBEL_5:5</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#NM6" title="WAYBEL_0:NM.6">Semilattice</a>  st  <a href="yellow_2.html#K2" title="YELLOW_2:func.2">SupMap</a> <font color="Olive" title="b1">L</font> is  <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>  &amp;  <a href="yellow_2.html#K2" title="YELLOW_2:func.2">SupMap</a> <font color="Olive" title="b1">L</font> is  <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a>  holds <br/> <a href="yellow_2.html#K2" title="YELLOW_2:func.2">SupMap</a> <font color="Olive" title="b1">L</font> is  <a href="waybel_1.html#V4" title="WAYBEL_1:attr.4">upper_adjoint</a> </div></div>
