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

Theorem Fabs_correct : forall x : float, Fabs x = Rabs x :>R.
intros x; unfold Rabs in |- *.