(** (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_nx_0_n : forall (n : nat) (x : Z), Mod (Z_of_nat n * x) 0 n.