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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</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="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">S</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/><b>let </b><font color="Maroon" title="c2">S</font> be  <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="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">S</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a></span><br/>



<a NAME="E1:40"/>
 <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="waybel23.html#D2" target="_self" title="WAYBEL23:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E2:40"/>
<font color="Maroon" title="c2">S</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 <b>by </b><i><a class="ref" href="yellow12.html#T27" title="YELLOW12:th.27">YELLOW12:27</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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