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

Lemma env_get_empty: forall id, env_get empty_env id = None.
Instance Join_env: Join env :=
fun (rho1 rho2 rho3: env) => join (env_get rho1) (env_get rho2) (env_get rho3).