case (Z_eq_dec Fnum1 Fnum2); intros H1.
case (Z_eq_dec Fexp1 Fexp2); intros H2.
left; apply floatEq; auto.
right; red in |- *; intros H'; Contradict H2; inversion H'; auto.
right; red in |- *; intros H'; Contradict H1; inversion H'; auto.
Qed.
Definition Fzero (x : Z) := Float 0 x.
Definition is_Fzero (x : float) := Fnum x = 0%Z.

(* Specifications: *)
Theorem is_FzeroP : forall x : float, is_Fzero x \/ ~ is_Fzero x.
unfold is_Fzero in |- *; intro; CaseEq (Fnum x); intros;
(right; discriminate) || (left; auto).