proposition: Lemma Forall_map_eq : forall (B:Type) (P:B->Prop) l (f:A -> B), Forall P (map f l) = Forall (fun x => P (f x)) l.
proof: Proof. Proof using. intros. extens. induction l; intros; rew_listx. { autos*. } { iff M; inverts* M. } Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)