Set of lower bounds in poset is defined like $ A^l = \{ x \in P : \forall a \in A . x \le a \} = \bigcap\_{a \in A} \{ x \in P : x \le a \}$. 


Is there in literature a name for union $ \bigcup\_{a \in A} \{ x \in P : x \le a \} $? 



Name for union of upsets/downsets
*Introduction to Lattices and Order* by B. A. Davey and H. A. Priestly calls this $\mathord{\downarrow}A$ or *the downset of $A$* and also uses $\mathord{\downarrow} a$ for $\{x \in P : x \le a\}$


