inversion H.
elim (mult_rel_prime a d (power d n));auto.
Qed.

(** if n>0 and m>0 then gcd(a^n,b^m)=1 iff gcd(a,b)=1 *)
Lemma power_power_rel_prime : forall (a n b m:nat),(n>0)->(m>0)->((rel_prime (power a n) (power b m))<->(rel_prime a b)).
split;intro.