(** 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 Zdigit_slice_out :
forall n k1 k2 k, (k2 <= k)%Z ->
Zdigit (Zslice n k1 k2) k = Z0.