(** Rational to the n-th power *)

Fixpoint Qcpower (q:Qc)(n:nat) : Qc :=
  match n with
    | O => 1
    | S n => q * (Qcpower q n)
  end.Notation " q ^ n " := (Qcpower q n) : Qc_scope.

(* Specifications: *)
Lemma Qcpower_1 : forall n, 1^n = 1.
Lemma Qcpower_0 : forall n, n<>O -> 0^n = 0.
Lemma Qcpower_pos : forall p n, 0 <= p -> 0 <= p^n.