intros x H'; unfold FNSucc in |- *; rewrite FcanonicFnormalizeEq; auto.
unfold FNPred in |- *; rewrite FSucPred; auto.
unfold FtoRradix in |- *; apply FnormalizeCorrect; auto.
apply FnormalizeCanonic; auto.
apply FNPredCanonic; auto.
Qed.

Theorem FNSucPredEq :
forall x : float,
Fcanonic radix b x -> FNSucc b radix precision (FNPred x) = x.