intros x y z H' H'0; repeat rewrite (Zmult_comm z);
apply Zle_Zmult_comp_r; auto.
Qed.

(* Specifications: *)
Theorem NotZmultZero :
forall z1 z2 : Z, z1 <> 0%Z -> z2 <> 0%Z -> (z1 * z2)%Z <> 0%Z.