(** l' is a permutation of l *)
Inductive is_permutation (A:Set) : list A->list A->Prop :=
  nil_is_permutation : (is_permutation A nil nil)
|cons_is_permutation : forall (l l':list A),(is_permutation A l l')->forall (x:A)(l'':(list A)),(insertion A x l' l'')->(is_permutation A (x::l) l'').(** l' is a permutation of l *)
Inductive is_permutation (A:Set) : list A->list A->Prop :=
  nil_is_permutation : (is_permutation A nil nil)
|cons_is_permutation : forall (l l':list A),(is_permutation A l l')->forall (x:A)(l'':(list A)),(insertion A x l' l'')->(is_permutation A (x::l) l'').(** l' is a permutation of l *)
Inductive is_permutation (A:Set) : list A->list A->Prop :=
  nil_is_permutation : (is_permutation A nil nil)
|cons_is_permutation : forall (l l':list A),(is_permutation A l l')->forall (x:A)(l'':(list A)),(insertion A x l' l'')->(is_permutation A (x::l) l'').

Lemma is_set_eq_impl_permutation : forall (A:Set)(l l':list A),(forall (x:A),(In x l)<->(In x l'))->(is_set A l)->(is_set A l')->(is_permutation A l l').