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<b>let </b><font color="Maroon" title="c1">L</font> be  <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#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>;<br/>

<a NAME="E1:41"/>
 <a href="yellow_2.html#K2" title="YELLOW_2:func.2">SupMap</a> <font color="Maroon" title="c1">L</font> <a href="waybel_1.html#NR8" title="WAYBEL_1:NR.8">has_a_lower_adjoint</a> 
 
<b>by </b><i><a class="ref" href="waybel_5.html#T3" title="WAYBEL_5:th.3">WAYBEL_5:3</a></i>;<br/>
<b>hence </b><a NAME="E2:41"/>
(  <a href="yellow_2.html#K2" title="YELLOW_2:func.2">SupMap</a> <font color="Maroon" title="c1">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="Maroon" title="c1">L</font> is <a href="waybel_0.html#V18" title="WAYBEL_0:attr.18">sups-preserving</a> )
 <b>by </b><i><a class="ref" href="waybel_1.html#T13" title="WAYBEL_1:th.13">WAYBEL_1:13</a>, <a class="ref" href="waybel_1.html#T60" title="WAYBEL_1:th.60">WAYBEL_1:60</a></i>;<br/>


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