intros p q H' H'0 H'1 H'2.
cut
((Fexp (Fopp q) < Fexp (Fopp p))%Z \/
Fexp (Fopp q) = Fexp (Fopp p) /\ (Fnum (Fopp q) < Fnum (Fopp p))%Z).
simpl in |- *.
intros H'3; elim H'3; clear H'3; intros H'3;
[ idtac | elim H'3; clear H'3; intros H'3 H'4 ]; auto;
right; split; auto with zarith.
apply FcanonicLtPos; try apply FcanonicFopp; auto; unfold FtoRradix in |- *;
repeat rewrite Fopp_correct; replace 0%R with (-0)%R;
auto with real.
Qed.

Theorem FcanonicFnormalizeEq :
forall p : float, Fcanonic p -> Fnormalize p = p.