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 incl_nth_error {X: Type} {Gamma Gamma': list X} :
incl Gamma Gamma' -> exists ξ, forall x, nth_error Gamma x = nth_error Gamma' (ξ x).