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_to_identy {A} `{asaA: Age_alg A}: forall k phi,
identity phi -> identity (age_to k phi).