(** * Exponential function with exponent in Z. *)

Definition ZExp (a n : Z) : Z :=
  match n with
  | Z0 => 1%Z
  | Zpos p => Exp a (nat_of_P p)
  | Zneg p => Exp a (nat_of_P p)
  end.

Lemma zexp_S1 : forall a n : Z, (0 <= n)%Z -> ZExp a (n + 1) = (a * ZExp a n)%Z.