(** Number of digits of a product.  This strong version is needed for proofs of division and square root algorithms, since they involve operation remainders. *)

Theorem Zdigits_div_Zpower :
forall m e,
(0 <= m)%Z ->
(0 <= e <= Zdigits m)%Z ->
Zdigits (m / Zpower beta e) = (Zdigits m - e)%Z.