apply Rabs_right; auto with real.
intros p0; apply Rabs_right; auto with real zarith.
intros p0; unfold IZR; rewrite <- INR_IPR; rewrite Rabs_Ropp.
apply Rabs_right; auto with real zarith.
Qed.

Theorem RmaxRmult :
forall p q r : R, (0 <= r)%R -> Rmax (r * p) (r * q) = (r * Rmax p q)%R.