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<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: WAYBEL_5:1</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#NM6" title="WAYBEL_0:NM.6">Semilattice</a> holds <br/> ( <font color="Olive" title="b1">L</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  iff  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> holds <br/> (  <a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <font color="Olive" title="b2">x</font> is   <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <font color="Olive" title="b1">L</font> &amp; <font color="Olive" title="b2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <font color="Olive" title="b2">x</font></span>)</span> &amp; (  for <font color="Olive" title="b3">I</font> being   <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Olive" title="b3">I</font> holds <br/> <a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <font color="Olive" title="b2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">I</font> ) ) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="waybel_5.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="txt" href="waybel_5.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/></div></div>
