Coercion seq_In T : seq T -> set T := fun s x => List.In x s.Coercion list_In T : list T -> set T := fun s x => List.In x s.

Lemma imset_bigcup_incl_l : forall {T U V : Type} (f : U -> V) (A : set T) (F : T -> set U), f @: (\bigcup_(x in A) F x) \subset \bigcup_(x in A) f @: F x.