(** [Qmin] and [Qmax] are obtained the usual way from [Qcompare]. *)

Definition Qmax := gmax Qcompare.Definition Qmin := gmin Qcompare.Module QMM := GenericMinMax Q_as_OT.Definition max := Qmax.Definition min := Qmin.Definition max_l := QMM.max_l.Definition max_r := QMM.max_r.Definition min_l := QMM.min_l.Definition min_r := QMM.min_r.

(* Specifications: *)
Lemma plus_max_distr_l : forall n m p, Qmax (p + n) (p + m) == p + Qmax n m.
Lemma plus_max_distr_r : forall n m p, Qmax (n + p) (m + p) == Qmax n m + p.
Lemma plus_min_distr_l : forall n m p, Qmin (p + n) (p + m) == p + Qmin n m.
Lemma plus_min_distr_r : forall n m p, Qmin (n + p) (m + p) == Qmin n m + p.