assert (forall (x n:nat),(In (x,n) l)->(In (x,n) l')).
apply factorisation_unique_upto_equiv_aux;trivial.
assert (forall (x n:nat),(In (x,n) l')->(In (x,n) l)).
apply factorisation_unique_upto_equiv_aux;auto.
apply is_set_eq_impl_permutation;intros;(try (apply pwd_impl_set;apply wf_impl_pwd;trivial));destruct x;split;auto.
Qed.
(** a list is a factorisation of n if l is well-formed and (refactor l)=n *)
Definition is_factorisation (n:nat)(l:list (nat*nat)) := (is_wf l)/\(n=(refactor l)).

(* Specifications: *)
(** The fondamental theorem of arithmetic *)
(** forall n<>0, there exists a factorisation l *)
Theorem factorisation_exists : forall (n:nat),n<>0->{l:list (nat*nat) | (is_factorisation n l)}.
intros.