intros z1 z2; case z1; case z2; simpl in |- *; auto with zarith.
Qed.

(* Specifications: *)
Theorem Zle_Zmult_comp_r :
forall x y z : Z, (0 <= z)%Z -> (x <= y)%Z -> (x * z <= y * z)%Z.
Theorem Zle_Zabs_inv1 :
forall z1 z2 : Z, (Zabs z1 <= z2)%Z -> (- z2 <= z1)%Z.