Fixpoint composeOptN' {A} (f : A -> option A) n x :=
match n with
| 0 => Some x
| S n =>
match composeOptN' f n x with
| Some y => f y
| None => None
end
end.

Lemma age_by_1 {A} {_ : ageable A} x : 0 < level x -> age x (age_by 1 x).