Definition lt (x y : ascii) := (N_of_ascii x < N_of_ascii y)%N.

(* Specifications: *)
Lemma lt_trans (x y z : ascii): lt x y -> lt y z -> lt x z.
Lemma lt_not_eq (x y : ascii): lt x y -> x <> y.
Local Lemma compare_helper_eq {a b : ascii} (E : cmp a b = Eq): a = b.
Local Lemma compare_helper_gt {a b : ascii} (G : cmp a b = Gt): lt b a.