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 age1_level0 {A} `{ageable A} : forall (x:A), age1 x = None <-> level x = 0.