#[global]
Instance min_compat : Proper (eq==>eq==>eq) min.

(* Specifications: *)
Lemma min_unicity n m p : ((n < m /\ p == n) \/ (m <= n /\ p == m)) -> p == min n m.
Lemma min_unicity_ext f : (forall n m, (n < m /\ f n m == n) \/ (m <= n /\ f n m == m)) -> (forall n m, f n m == min n m).
Lemma min_mono f : (Proper (eq ==> eq) f) -> (Proper (le ==> le) f) -> forall x y, min (f x) (f y) == f (min x y).
Lemma min_id n : min n n == n.