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_set_eq: forall (U T : Type) (s1 s2 : set U) (f : U -> T), f @: (s1 :|: s2) <--> f @: s1 :|: f @: s2.