(** 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_ge :
forall x y,
(x <> 0)%Z -> (y <> 0)%Z ->
(Zdigits x + Zdigits y - 1 <= Zdigits (x * y))%Z.