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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#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">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<a NAME="E1:45"/>
 <a href="yellow_0.html#R1" target="_self">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:45"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1" target="_self">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">L</font> iff ( <font color="Maroon">a</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X</font> &amp; ( for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">b</font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">X</font> holds <br/><font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b</font> ) ) )
 <b>by </b><i/>;<br/>


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