Section ForallNorm.
Variable T : Type.
Variable P : T -> Prop.
(* use: rewrite ?Forall_norm *)
Definition Forall_norm := (@Forall_appP, @Forall_singletonP, @Forall_consP, @Forall_nilP).

Lemma in_app_l {X: Type} {x: X} {l1 l2: list X} : In x l1 -> In x (l1 ++ l2).