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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E47">Th49</font></span>: <a NAME="T49"><span class="comment"><font color="firebrick">:: WAYBEL_2:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a> holds <br/> ( <font color="Olive" title="b1">L</font> is  <a href="waybel_2.html#V2" title="WAYBEL_2:attr.2">meet-continuous</a>  iff (  <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#V19" title="WAYBEL_0:attr.19">meet-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#V20" title="WAYBEL_0:attr.20">join-preserving</a>  ) )</div></div>
