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<div><span class="kw">theorem </span><a NAME="T49"><span class="comment"><font color="firebrick">:: WAYBEL23:49</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><br/>  for <font color="Olive" title="b2">B</font> being   <a href="waybel23.html#V2" title="WAYBEL23:attr.2">join-closed</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font>  st  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Olive" title="b1">L</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">B</font> holds <br/>( <font color="Olive" title="b2">B</font> is    <a href="waybel23.html#M1" title="WAYBEL23:mode.1">CLbasis</a> of <font color="Olive" title="b1">L</font> iff  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  st  not <font color="Olive" title="b4">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b3">x</font> holds <br/> ex <font color="Olive" title="b5">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> st <br/>( <font color="Olive" title="b5">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">B</font> &amp;  not <font color="Olive" title="b5">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b3">x</font> &amp; <font color="Olive" title="b5">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b4">y</font> ) )</div></div>
