induction i;intros a T;case T;simpl;intros;try (rewrite IHi);simpl;reflexivity.
Defined.
Definition map (S:Store A) : Store B :=
mkStore (index S) (Tmap (contents S)).

(* Specifications: *)
Lemma get_map: forall i S,
get i (map S)= match get i S with PNone => PNone
| PSome a => PSome (f a) end.