apply lt_IZR.
apply (Rlt_monotony_contra_exp radix) with (z := Fexp p);
auto with real arith.
simpl in |- *; rewrite Rmult_0_l; auto.
Qed.

(* Specifications: *)
Theorem LeR0Fnum : forall p : float, (0 <= p)%R -> (0 <= Fnum p)%Z.
intros p H'.
Theorem R0LeFnum : forall p : float, (p <= 0)%R -> (Fnum p <= 0)%Z.
intros p H'.