Section Fcore_digits.
Variable beta : radix.
Definition Zdigit n k := Z.rem (Z.quot n (Zpower beta k)) beta.
Fixpoint Zsum_digit f k :=
match k with
| O => Z0
| S k => (Zsum_digit f k + f (Z_of_nat k) * Zpower beta (Z_of_nat k))%Z
end.
(** 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 Zsame_sign_scale :
forall n k,
(0 <= n * Zscale n k)%Z.