split. exact addZ_commutativity.
split. exact Z_group.
split. unfold intern in |- *. intros. exact I.
split. exact multZ_associativity. exact mult_add_distributivity.
Qed.

(*********************************)
Theorem Z_unitary_commutative_ring :
is_unitary_commutative_ring Z IdZ addZ multZ OZ IZ oppZ.