intros x H'.
apply FcanonicUnique with (precision := precision) (5 := H'); auto.
apply FNPredCanonic; auto with float.
apply FcanonicBound with (radix := radix); auto.
apply FNSuccCanonic; auto.
apply FcanonicBound with (radix := radix); auto.
apply FNPredSuc; auto.
apply FcanonicBound with (radix := radix); auto.
Qed.

Theorem FNSucPred :
forall x : float,
Fbounded b x -> FNSucc b radix precision (FNPred x) = x :>R.