Section BIJECTION.
Variable A B : Type.
Variable ag: ageable A.
Variable bijAB: bijection A B.
Let levelB (x:B) : nat :=
level (bij_g _ _ bijAB x).
Let age1B  (x: B) : option B :=
match age1 (bij_g _ _ bijAB x) with
| Some y => Some (bij_f _ _ bijAB y)
| None => None
end.
Let ageB (x y: B) :=age1B x = Some y.

Lemma age_bij_level2 :
forall x y, age1B x = Some y -> levelB x = S (levelB y).