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 map_0P {X: Type} {A: list X} : (map (fun=> 0) A) = repeat 0 (length A).