apply Rabs_left; auto.
rewrite H1; simpl in |- *; rewrite Rabs_right; auto with real.
Qed.

Theorem RmaxLess1 : forall r1 r2 : R, (r1 <= Rmax r1 r2)%R.
intros r1 r2; unfold Rmax in |- *; case (Rle_dec r1 r2); auto with real.