simpl.
apply nil_is_permutation.
simpl.
eapply cons_is_permutation.
apply IHl.
apply insertion_snoc.
Qed.

Lemma is_permutation_reverse_impl_is_permutation : forall (A:Set)(l l':list A),(is_permutation A (rev l) (rev l'))->(is_permutation A l l').
intros.