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 Forall_appI {A B}: Forall P A -> Forall P B -> Forall P (A ++ B).