Section Facts.
(* usage: rewrite ? Forall_norm *)
Definition Forall_norm := (@Forall_app_iff, @Forall_singleton_iff, @Forall_cons_iff, @Forall_nil_iff).

Lemma Forall_repeat {X: Type} {a} {A: list X} : Forall (fun b => a = b) A -> A = repeat a (length A).