intros x; case x; unfold FtoRradix, FtoR in |- *; simpl in |- *.
intros Fnum1 Fexp1 H'.
repeat rewrite <- (Rmult_comm (powerRZ radix Fexp1)); apply Rmult_eq_compat_l;
auto.
cut (0 <= Fnum1)%Z.
unfold Zabs, Zle in |- *.
case Fnum1; simpl in |- *; auto.
intros p H'0; case H'0; auto.
apply Znot_gt_le; auto.
Contradict H'.
apply Rgt_not_le; auto.
rewrite Rmult_comm.
replace 0%R with (powerRZ radix Fexp1 * 0)%R; auto with real.
red in |- *; apply Rmult_lt_compat_l; auto with real zarith.
Qed.

Theorem Fabs_correct2 :
forall x : float, (FtoR radix x <= 0)%R -> Fabs x = (- x)%R :>R.