Arguments af_wf [A] _ _.
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.