(* 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 Zeq_mult_simpl : forall a b c : Z, c <> 0%Z -> (a * c)%Z = (b * c)%Z -> a = b.