Module Import Private_Tac := !MakeOrderTac O O.
(** An alternative characterisation of [max], equivalent to [max_l /\ max_r] *)
(** A more symmetric version of [max_spec], based only on [le]. Beware that left and right alternatives overlap. *)
Instance : Proper (eq==>eq==>iff) le.
(** A function satisfying the same specification is equal to [max]. *)
(** [max] commutes with monotone functions. *)

Lemma max_mono f :
(Proper (eq ==> eq) f) ->
(Proper (le ==> le) f) ->
forall x y, max (f x) (f y) == f (max x y).