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_last {A} i l (a x : A) :
i = length l ->
upd i x (l ++ a :: nil) = Some (l ++ x :: nil).