(** ** Qpower and exponent multiplication *)

(* Specifications: *)
Lemma Qpower_mult_positive : forall a n m,
Qpower_positive a (n*m) == Qpower_positive (Qpower_positive a n) m.
Lemma Qpower_mult : forall a n m, a^(n*m) ==  (a^n)^m.
(** ** Qpower decomposition *)
Lemma Qpower_decomp_pos: forall (p : positive) (a : Z) (b : positive),
(a # b) ^ (Z.pos p) == a ^ (Z.pos p) # (b ^ p)%positive.
Lemma Qpower_decomp_neg_pos: forall (p a b: positive),
(Z.pos a # b) ^ (Z.neg p) == (Z.pos b) ^ (Z.pos p) # (a ^ p)%positive.
Lemma Qpower_decomp_neg_neg: forall (p a b: positive),
(Z.neg a # b) ^ (Z.neg p) == (Z.neg b) ^ (Z.pos p) # (a ^ p)%positive.