Fixpoint upd (i : nat) {A} new (l : list A) : option (list A) :=
  match i, l with
  | O, _ :: l => Some (new :: l)
  | _, nil => None
  | S i, x :: l =>
    match upd i new l with
    | Some l' => Some (x :: l')
    | None => None
    end
  end.

Lemma upd_rev {A} i x (l : list A) : (i < length l)%nat -> upd i x (rev l) = option_map (@rev A) (upd (length l - 1 - i) x l).