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(* 02110-1301 USA                                                     *)
(** modulo Modulo Arithmetic.  @author Olga Caprotti and Martijn Oostdijk @version $Revision$ *)
(** (Mod a b n) means (a = b (mod n)) *)
Definition Mod (a b : Z) (n : nat) :=
exists q : Z, a = (b + Z_of_nat n * q)%Z.

Lemma mod_repr_non_0 :
forall (n : nat) (x : Z), (0 < x < Z_of_nat n)%Z -> ~ Mod x 0 n.