Module NBaseProp (Import N : NAxiomsMiniSig').
(** First, we import all known facts about both natural numbers and integers. *)
Include NZProp N.
(** From [pred_0] and order facts, we can prove that 0 isn't a successor. *)
(** Next, we show that all numbers are nonnegative and recover regular induction from the bidirectional induction on NZ *)

Theorem induction :
forall A : N.t -> Prop, Proper (N.eq==>iff) A ->
A 0 -> (forall n, A n -> A (S n)) -> forall n, A n.