Definition exp : Z -> U -> U.
Hint Resolve exp_endo.

(* Specifications: *)
Lemma exp_unfold_pos :
forall (a : U) (n : nat),
In U G a -> exp (pos (S n)) a = star a (exp (pos n) a).
Lemma exp_unfold_neg :
forall (a : U) (n : nat),
In U G a -> exp (neg (S n)) a = star (inv a) (exp (neg n) a).
Lemma exp_l1 :
forall (a : U) (n : nat),
In U G a -> star a (exp (neg (S n)) a) = exp (neg n) a.