Definition age_induction {A} `{ageable A} :=
  well_founded_induction (af_wf _).Definition fashionR {A1} `{ageable A1} {A2}`{ageable A2} (x:A1) (y: A2) : Prop :=
  level x = level y.

Lemma age_level {A} `{ageable A} : forall (x y:A), age x y -> level x = S (level y).