proposition: Lemma map_ext_in {A B} (f f' : A -> B) (ls : list A) (H : forall a, List.In a ls -> f a = f' a) : List.map f ls = List.map f' ls.
proof: Proof. induction ls; simpl; trivial. rewrite H, IHls. { reflexivity. } { intros; apply H; right; assumption. } { left; reflexivity. } 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