intros p H'.
unfold FtoRradix, FtoR, Fabs in |- *; simpl in |- *.
apply Rmult_le_compat_r; auto with real arith.
rewrite Zabs_absolu.
replace 1%R with (INR 1); auto with real.
repeat rewrite <- INR_IZR_INZ; apply Rle_INR; auto.
cut (Zabs_nat (Fnum p) <> 0); auto with zarith.
Contradict H'.
unfold FtoRradix, FtoR in |- *; simpl in |- *.
replace (Fnum p) with 0%Z; try (simpl;ring).
generalize H'; case (Fnum p); simpl in |- *; auto with zarith arith;
intros p0 H'3; Contradict H'3; auto with zarith arith.
Qed.

(* Specifications: *)
Theorem Fabs_Fzero : forall x : float, ~ is_Fzero x -> ~ is_Fzero (Fabs x).
intros x; case x; unfold is_Fzero in |- *; simpl in |- *.