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

Lemma nth_consP {X: Type} {n} {a b: X} {A}: nth (S n) (a :: A) b = nth n A b.