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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM6" title="WAYBEL_0:NM.6">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 non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">S</font> is   <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font> iff <font color="Olive" title="b1">S</font> is <a href="waybel23.html#V1" title="WAYBEL23:attr.1">meet-closed</a> )</span><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#V13" title="WAYBEL_0:attr.13">upper</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#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font> iff <font color="Maroon" title="c2">S</font> is <a href="waybel23.html#V1" title="WAYBEL23:attr.1">meet-closed</a> )</span><br/>



<a NAME="E1:43"/>
( <font color="Maroon" title="c2">S</font> is   <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</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#V5" title="YELLOW_0:attr.5">meet-inheriting</a> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#T63" title="WAYBEL_0:th.63">WAYBEL_0:63</a></i>;<br/>
<b>hence </b><a NAME="E2:43"/>
( <font color="Maroon" title="c2">S</font> is   <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font> iff <font color="Maroon" title="c2">S</font> is <a href="waybel23.html#V1" title="WAYBEL23:attr.1">meet-closed</a> )
 <b>by </b><i><a class="ref" href="waybel23.html#D1" target="_self" title="WAYBEL23:def.1">Def1</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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