intros x y H'; cut ((x - y)%R = 0%R).
rewrite <- Fdiff_correct; intros H'1; case Rmult_integral with (1 := H'1).
intros H'0; unfold Feq_bool, Fcompare in |- *.
rewrite eq_IZR_R0 with (1 := H'0); auto.
intros H'0; Contradict H'0.
case (Zmin (Fexp x) (Fexp y)); simpl in |- *; auto with real zarith.
apply Rplus_eq_reg_l with (r := FtoR radix y); auto with real.
Qed.

Theorem Feq_bool_correct_f :
forall x y : float, Feq_bool x y = false -> ~ Feq x y.