intros p H'.
replace (Fulp p) with (powerRZ radix (Fexp p)).
2: unfold Fulp in |- *; replace (Fnormalize radix b precision p) with p; auto;
apply sym_equal; apply FcanonicUnique with (3 := pGivesBound);
auto with arith; apply FnormalizeCanonic || apply FnormalizeCorrect;
auto with arith.
unfold FtoRradix in |- *; rewrite <- Fminus_correct; auto with arith.
case (Z_eq_dec (Fnum p) (nNormMin radix precision)); intros H1'.
case (Z_eq_dec (Fexp p) (- dExp b)); intros H2'.
rewrite FPredDiff2; auto with arith.
unfold FtoR in |- *; simpl in |- *; rewrite Rmult_1_l; auto with real.
rewrite FPredDiff3; auto with arith.
unfold FtoR in |- *; simpl in |- *; rewrite Rmult_1_l; auto with real.
apply Rlt_le; apply Rlt_powerRZ; auto with real zarith.
replace 1%R with (INR 1); auto with real arith.
unfold Zpred in |- *; auto with zarith.
rewrite FPredDiff1; auto with arith.
unfold FtoR in |- *; simpl in |- *; rewrite Rmult_1_l; auto with real.
apply FcanonicBound with (1 := H').
Qed.

Theorem FulpPred :
forall p : float,
Fbounded b p -> (p - FNPred b radix precision p <= Fulp p)%R.