- 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.

Lemma Rmax_assoc : forall a b c, Rmax a (Rmax b c) = Rmax (Rmax a b) c.