proposition: Lemma forall_In_map {A B} {P : B -> Prop} (f : A -> B) ls : (forall x, List.In x (List.map f ls) -> P x) <-> (forall x, List.In x ls -> P (f x)).
proof: Proof. induction ls as [|?? IHls]; simpl; intuition (subst; auto). Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.ZArith.ZArith Coq.Lists.List Coq.Lists.SetoidList Coq.Bool.Bool Fiat.Common Fiat.Common.List.Operations Fiat.Common.Equality Fiat.Common.List.FlattenList Fiat.Common.LogicFacts