case H3;intro.
rewrite H4 in H2.
rewrite H4 in H1;inversion H1.
generalize (rel_prime_power p (refactor l) n (rel_prime_sym p (refactor l) H11));intro.
rewrite mult_comm in H2.
generalize (gauss (power p n) (refactor l) (power p m) H12 H2);intro.
apply power_divides_power with p;trivial.
destruct p.
elim (not_prime_zero H8).
elim H8;omega.
destruct a.
inversion H1.
apply IHl;trivial.
apply gauss with (power n0 n1);trivial.
apply rel_prime_power;apply rel_prime_sym;apply rel_prime_power.
apply (rel_prime_wf l p m n0 n1);trivial.
Qed.

(* Specifications: *)
(** if l and l' are well-formed and (refactor l)=(refactor l') then l is included in l' *)
Lemma factorisation_unique_upto_equiv_aux : forall (l l':list (nat*nat)),(is_wf l)->(is_wf l')->(refactor l)=(refactor l')->(forall (x n:nat),(In (x,n) l)->(In (x,n) l')).
intros l l';intro;intro;intro;intros p n;intro.