unfold rel_prime;apply gcd_sym;apply gcd_one.
generalize (IHn H);intro.
apply rel_prime_mult;trivial.
Qed.

(** if n>0 and gcd(a,d^n)=1 then gcd(a,d)=1 *)
Lemma power_rel_prime : forall (d a n:nat),(n>0)->(rel_prime a (power d n))->(rel_prime a d).
destruct n;simpl;intros.