#[global]
Instance : Proper (eq==>eq==>iff) le.#[global]
Instance max_compat : Proper (eq==>eq==>eq) max.

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).