intros p r; try assumption.
apply
Trans with (group_inverse G (nat_to_group r (nat_of_P (pos_abs (ax3 p)))));
auto with algebra.
apply
Trans with (nat_to_group (group_inverse G r) (nat_of_P (pos_abs (ax3 p))));
auto with algebra.
Qed.
Hint Resolve Z_to_group_nat_neg: algebra.

Lemma Z_to_group_nat_inv :
forall (n : Z) (r : G),
Equal (Z_to_group_nat_fun r (- n)%Z)
(Z_to_group_nat_fun (group_inverse G r) n).