(** (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.