Inductive powers (a : U) : Ensemble U :=
    In_powers : forall (m : Z) (x : U), x = exp m a -> In U (powers a) x.Inductive powers (a : U) : Ensemble U :=
    In_powers : forall (m : Z) (x : U), x = exp m a -> In U (powers a) x.

Theorem powers_of_one_element : forall a : U, In U G a -> Setsubgroup U (powers a) Gr.