proposition: Fact Rmax3_def : forall x y z, Rmax3 x y z = Rmax2 (Rmax2 x y) z.
proof: Proof. intros x y z; unfold Rmax2; unfold Rmax3. destruct (total_order_T x y) as [[xLy | xEy] |xGy]; destruct (total_order_T y z) as [[yLz | yEz] |yGz]; destruct (total_order_T x z) as [[xLz | xEz] |xGz]; lra. Qed.
imports: Reals Psatz