intros p q H' H'0 H'1.
rewrite <- (Ropp_involutive p); rewrite <- (Ropp_involutive q);
apply Ropp_eq_compat.
unfold FtoRradix in |- *; repeat rewrite <- Fopp_correct.
apply FSuccZleEq with (b := b) (precision := precision); auto.
repeat rewrite Fopp_correct; auto with real.
apply Ropp_lt_cancel.
repeat rewrite <- Fopp_correct; rewrite <- FPredFopFSucc; rewrite Fopp_Fopp;
auto.
Qed.
Definition FNPred (x : float) := FPred (Fnormalize radix b precision x).

Theorem FNPredFopFNSucc :
forall x : float, FNPred x = Fopp (FNSucc b radix precision (Fopp x)).