(** Left and right shifts *)

Definition Zscale n k :=
  if Zle_bool 0 k then (n * Zpower beta k)%Z else Z.quot n (Zpower beta (-k)).

Theorem Zscale_scale : forall n k k', (0 <= k)%Z -> Zscale (Zscale n k) k' = Zscale n (k + k').