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 \} $?
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 \} $? 


Introduction to Lattices and Order by B. A. Davey and H. A. Priestly calls this $\downarrow A$—the downset of $A$—and also uses $\downarrow a$ for $\{x \in P : x \le a\}$ 

