Definition pow_N (x:R) (p:N) :=
match p with
| N0 => rI
| Npos p => pow_pos x p
end.
Definition id_phi_N (x:N) : N := x.

(* Specifications: *)
Lemma pow_N_pow_N x n : pow_N x (id_phi_N n) == pow_N x n.
End Power.