(* 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 necR_age_by_iff {A} `{agA : ageable A} x x' : necR x x' <-> x' = age_by (level x - level x') x.