Section Fcore_digits.
Variable beta : radix.
Definition Zdigit n k := Z.rem (Z.quot n (Zpower beta k)) beta.

Theorem Zdigit_div_pow :
forall n k k', (0 <= k)%Z -> (0 <= k')%Z ->
Zdigit (Z.quot n (Zpower beta k')) k = Zdigit n (k + k').