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. *)
(** *** Semi-lattice algebraic properties of [max] *)
Notation max_idempotent := max_id (only parsing).

Lemma max_assoc m n p : max m (max n p) == max (max m n) p.