#[global]
Instance : Proper (eq==>eq==>iff) le.
(** A function satisfying the same specification is equal to [max]. *)

(* Specifications: *)
Lemma max_unicity n m p :
((n < m /\ p == m) \/ (m <= n /\ p == n)) -> p == max n m.
Lemma max_unicity_ext f :
(forall n m, (n < m /\ f n m == m) \/ (m <= n /\ f n m == n)) ->
(forall n m, f n m == max n m).