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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="waybel_0.html#V12" title="WAYBEL_0:attr.12">lower</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>



<a NAME="E1:44"/>
( <font color="Maroon" title="c2">S</font> is   <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <font color="Maroon" title="c1">L</font> iff  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">S</font> is <a href="yellow_0.html#V6" title="YELLOW_0:attr.6">join-inheriting</a> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#T64" title="WAYBEL_0:th.64">WAYBEL_0:64</a></i>;<br/>
<b>hence </b><a NAME="E2:44"/>
( <font color="Maroon" title="c2">S</font> is   <a href="waybel_0.html#NM3" title="WAYBEL_0:NM.3">Ideal</a> of <font color="Maroon" title="c1">L</font> iff <font color="Maroon" title="c2">S</font> is <a href="waybel23.html#V2" title="WAYBEL23:attr.2">join-closed</a> )
 <b>by </b><i><a class="ref" href="waybel23.html#D2" target="_self" title="WAYBEL23:def.2">Def2</a></i>;<br/>


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