(* Age [x] to the level [k] (meaningul when [k <= level x] *)
Definition age_to k {A} `{agA : ageable A} (x : A) : A := age_by (level x - k) x.

Lemma iter_iter n m {A} f (x : A) : Nat.iter n f (Nat.iter m f x) = Nat.iter (n + m) f x.