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_union_incl {U T : Type} (s1 s2 : set U) (f : U -> T) : f @: (s1 :|: s2) \subset (f @: s1) :|: (f @: s2).