Definition cmp : string -> string -> comparison := String.compare.

(* Specifications: *)
Lemma cmp_eq (a b : string): cmp a b = Eq <-> a = b.
Lemma cmp_antisym (a b : string): cmp a b = CompOpp (cmp b a).
Lemma cmp_lt (a b : string): cmp a b = Lt <-> lt a b.
Local Lemma compare_helper_lt {a b : string} (L : cmp a b = Lt): lt a b.
Local Lemma compare_helper_gt {a b : string} (G : cmp a b = Gt): lt b a.
Local Lemma compare_helper_eq {a b : string} (E : cmp a b = Eq): a = b.