(** 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_mult_strong :
forall x y,
(0 <= x)%Z -> (0 <= y)%Z ->
(Zdigits (x + y + x * y) <= Zdigits x + Zdigits y)%Z.