unfold compare; intros x y H.
rewrite <- ascii_N_embedding with (a := x);
rewrite <- ascii_N_embedding with (a := y).
f_equal.
now apply N.compare_eq_iff.
Qed.

(* Specifications: *)
Lemma compare_same_is_eq : forall (x : Ascii.ascii), compare x x = Eq.
intro x; unfold compare.