(* We cannot prove that the predecessor is injective, nor that it is left-inverse to the successor at this point *)
Variable A : t -> Prop.
Hypothesis A_wd : Proper (eq==>iff) A.

(* Specifications: *)
Theorem central_induction :
forall z, A z ->
(forall n, A n <-> A (S n)) ->
forall n, A n.