auto.
intros.
inversion H1.
subst x0;subst l0.
eapply insertion_is_set.
apply IHis_permutation.
auto.
elim (permutation_in _ _ _ H x).
intros.
red;intro.
apply H5.
apply H3.
apply H6.
auto.
Qed.

Lemma Permutation_impl_permutation : forall (A:Set)(l l':list A),(Permutation l l')->(is_permutation _ l l').
induction 1.