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_seqP {P : nat -> Prop} {m n: nat} :
Forall P (seq m n) <-> (forall i, m <= i < m + n -> P i).