intros p H.
replace (FtoRradix p) with (FtoRradix (Fnormalize radix b precision p));
[ idtac | unfold FtoRradix in |- *; apply FnormalizeCorrect; auto ].
unfold FtoRradix in |- *; rewrite <- Fabs_correct; auto with arith real.
unfold FtoR in |- *; simpl in |- *; unfold Fulp in |- *.
apply Rmult_le_compat_r; [ apply powerRZ_le | idtac ];
auto with real arith zarith.
apply Rle_trans with (IZR (Zpred (Zpos (vNum b))));
[ apply Rle_IZR; auto with float zarith | idtac ].
unfold Zpred in |- *; right; rewrite pGivesBound; replace 1%R with (IZR 1);
auto with real.
rewrite <- Zpower_nat_Z_powerRZ; rewrite Z_R_minus;auto.
Qed.

Theorem LeFulpPos :
forall x y : float,
Fbounded b x ->
Fbounded b y -> (0 <= x)%R -> (x <= y)%R -> (Fulp x <= Fulp y)%R.