intros p q H' H'0 H'1 H'2.
rewrite <- (Ropp_involutive p); rewrite <- (Ropp_involutive q).
apply Ropp_gt_lt_contravar; red in |- *.
unfold FtoRradix in |- *; repeat rewrite <- Fopp_correct.
apply FsubnormalnormalLtPos; auto.
apply FsubnormFopp; auto.
apply FnormalFop; auto.
unfold FtoRradix in |- *; rewrite Fopp_correct; replace 0%R with (-0)%R;
auto with real.
unfold FtoRradix in |- *; rewrite Fopp_correct; replace 0%R with (-0)%R;
auto with real.
Qed.
Definition Fnormalize (p : float) :=
match Z_zerop (Fnum p) with
| left _ => Float 0 (- dExp b)
| right _ =>
Fshift radix
(min (precision - Fdigit radix p) (Zabs_nat (dExp b + Fexp p))) p
end.

Theorem FnormalizeCorrect : forall p : float, Fnormalize p = p :>R.
intros p; unfold Fnormalize in |- *.