eapply is_permutation_trans.
apply is_permutation_reverse.
apply is_permutation_sym.
eapply is_permutation_trans.
apply is_permutation_reverse.
apply is_permutation_sym.
trivial.
Qed.

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