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

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