(* Apply [age1] n times (meaningful when [n <= level x] *)

Definition age1' {A} `{agA : ageable A} : A -> A :=
  fun x => match age1 x with Some y => y | None => x end.Definition age_by n {A} `{agA : ageable A} : A -> A := Nat.iter n age1'.

Lemma level_age_by n {A} `{agA : ageable A} x : level (age_by n x) = level x - n.