intros e n; elim n; unfold Zpower_nat in |- *; simpl in |- *;
auto with zarith.
Qed.
Hint Resolve Zpower_NR0 Zpower_NR1: zarith.
(* To define exponential over relative number, we simply do a case analysis on the sign of the number *)
Definition powerRZ (e : R) (n : BinInt.Z) :=
match n with
| BinInt.Z0 => 1%R
| BinInt.Zpos p => (e ^ BinPos.nat_of_P p)%R
| BinInt.Zneg p => (/ e ^ BinPos.nat_of_P p)%R
end.
(* we now prove some basic properties of our exponential *)

(* Specifications: *)
Theorem powerRZ_O : forall e : R, powerRZ e 0 = 1%R.
simpl in |- *; auto.