- now intros w; rewrite Rmax_left;[ | apply Rge_le, Ropp_le_ge_contravar].
- now intros w; rewrite Rmax_right; [ | apply Rge_le, Ropp_le_ge_contravar].
Qed.

(* Specifications: *)
Lemma Rmax_assoc : forall a b c, Rmax a (Rmax b c) = Rmax (Rmax a b) c.
Lemma Rminmax : forall a b, Rmin a b <= Rmax a b.
Lemma Rmin_assoc : forall x y z, Rmin x (Rmin y z) =
Rmin (Rmin x y) z.