intros p; case p; unfold Fnormalize in |- *; simpl in |- *.
intros Fnum1 Fexp1; case (Z_zerop Fnum1); intros H'.
rewrite H'; simpl in |- *; auto.
case (Z_zerop (- Fnum1)); intros H'0; simpl in |- *; auto.
case H'; replace Fnum1 with (- - Fnum1)%Z; auto with zarith.
unfold Fopp, Fshift, Fdigit in |- *; simpl in |- *.
replace (digit radix (- Fnum1)) with (digit radix Fnum1).
apply floatEq; simpl in |- *; auto with zarith.
ring.
case Fnum1; simpl in |- *; auto.
Qed.

Theorem FnormalizeBounded :
forall p : float, Fbounded b p -> Fbounded b (Fnormalize p).