case_eq (Char.compare a b); simpl; try congruence.
now intros Hab Hxy; rewrite (Char.compare_implies_eq _ _ Hab); rewrite (HI _ Hxy).
Qed.

(* Specifications: *)
Lemma compare_same_is_eq : forall (x : t), compare x x = Eq.
intro x; induction x; simpl; trivial.