destruct rho.
unfold finite_idfun, finMap in *.
generalize f; intros [l ?].
exists l; simpl in *.
intros; unfold compose in *.
apply e; auto.
Qed.

Lemma Join_env_eq: Join_env = Join_fpm (Join_prod _ Join_pshare _ JA).
Instance Perm_env {PA: Perm_alg A}: @Perm_alg env Join_env.