(* The property of a  number to divide another one 
     (Ndivides n m) shoud be read as m divides n *)
 
Definition Zdivides (n m : Z) := exists q : Z, n = (m * q)%Z.

Theorem ZdividesDiv : forall n m p : Z, p <> 0%Z -> Zdivides (p * n) (p * m) -> Zdivides n m.