Definition finite_idfun (f: key -> option (pshare * A)) :=
          (exists l, forall a, ~In a l -> f a = None).Definition mk_env_aux: forall f, finite_idfun f -> finMap f.Definition mk_env (f: key -> option (pshare * A))  (FIN: finite_idfun f):  env :=
   exist _ _ (mk_env_aux _ FIN).

Lemma finite_idfun_empty: finite_idfun (fun _ => None).