(** 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 Zdigit_scale : forall n k k', (0 <= k')%Z -> Zdigit (Zscale n k) k' = Zdigit n (k' - k).