(** 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).