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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V3">complete</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel23.html#V4" target="_self">sups-closed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/>





<a NAME="E1:38"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>
<b>hence </b><a NAME="E2:38"/>
 <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">L</font>
 <b>by </b><i/>;<br/>


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