(** Anti-monotonicity swaps the role of [min] and [max] *)

(* Specifications: *)
Lemma max_min_antimono f :
Proper (eq==>eq) f ->
Proper (le==>flip le) f ->
forall x y, max (f x) (f y) == f (min x y).
Lemma min_max_antimono f :
Proper (eq==>eq) f ->
Proper (le==>flip le) f ->
forall x y, min (f x) (f y) == f (max x y).