intros H'0; apply lt_le_weak; apply lt_Rlt; auto.
intros H'0; rewrite <- (INR_inv _ _ H'0); auto with arith.
Qed.

(* Specifications: *)
Theorem Rmult_IZR : forall z t : Z, IZR (z * t) = (IZR z * IZR t)%R.
intros z t; case z; case t; simpl in |- *; auto with real; unfold IZR; intros t1 z1; repeat rewrite <- INR_IPR.