(** Slice of an integer *)
Definition Zslice n k1 k2 :=
if Zle_bool 0 k2 then Z.rem (Zscale n (-k1)) (Zpower beta k2) else Z0.

Theorem Zslice_div_pow :
forall n k k1 k2, (0 <= k)%Z -> (0 <= k1)%Z ->
Zslice (Z.quot n (Zpower beta k)) k1 k2 = Zslice n (k1 + k) k2.