intros P n p HP H'.
case (ZroundZ P (Z_of_nat n) p); auto.
repeat rewrite <- INR_IZR_INZ; auto.
intros x H'0; exists (Zabs_nat x).
rewrite <- (inj_abs x) in H'0.
rewrite H'0.
repeat rewrite <- INR_IZR_INZ; auto.
apply le_IZR; simpl in |- *.
rewrite <- H'0; auto.
apply RleRoundedR0 with (P := P) (r := INR n); auto.
replace 0%R with (INR 0); auto with real arith.
Qed.
(* Properties of LSB and MSB *)

Theorem FUlp_Le_LSigB :
forall x : float, Fbounded b x -> (Fulp x <= Float 1%nat (LSB radix x))%R.