Proof with auto.
intros.
unfold upd.
case (eq_dec a a)...
intro.
destruct n...
Qed.
Arguments upd_eq [A H B] _ _ _.

(* Specifications: *)
Lemma upd_eq' {A} `{EqDec A} : forall B (f : A -> B) a b a',
a = a' ->
upd f a b a' = b.