Hint Resolve exp_l2 exp_l2' exp_unfold_pos exp_unfold_neg.
Hint Immediate sym_eq.

(* Specifications: *)
Theorem add_exponents :
forall (a : U) (m n : Z),
In U G a -> star (exp m a) (exp n a) = exp (addZ m n) a.
Lemma exp_commut1 :
forall (a : U) (m : Z), In U G a -> star (exp m a) a = star a (exp m a).
Lemma tech_opp_pos_negZ1 : forall n : nat, oppZ (pos n) = neg n.
Lemma tech_opp_pos_negZ2 : forall n : nat, oppZ (neg n) = pos n.
Theorem change_exponent_sign :
forall (a : U) (m : Z), In U G a -> inv (exp m a) = exp (oppZ m) a.