In this talk we show that a non-collapsed metric measure space which satisfies the synthetic Ricci curvature CD (K,n) in the sense of Lott-Sturm-Villani, and which has curvature bounded from above by k in the sense of Alexandrov, is an Alexandrov space with curvature bounded from below by K- (n-2)k. This is a joint work with Vitali Kapovitch.