intros x H.
unfold FtoRradix in |- *; apply FSuccDiff1; auto with arith.
Contradict H; unfold FtoRradix, FtoR in |- *; simpl in |- *; rewrite H.
apply Rlt_not_le.
replace 0%R with (0 * powerRZ radix (Fexp x))%R; [ idtac | ring ].
apply Rlt_monotony_exp; auto with real arith.
generalize (nNormPos _ radixMoreThanOne precision);
replace 0%R with (IZR (- 0%nat)); auto with real zarith arith.
Qed.

(* Specifications: *)
Theorem FulpFPredGePos :
forall f : float,
Fbounded b f ->
Fcanonic radix b f ->
(0 < f)%R -> (Fulp (FPred b radix precision f) <= Fulp f)%R.