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).

(* Specifications: *)
Lemma env_get_mk_env: forall (f: key -> option (pshare * A)) P, env_get (mk_env f P) = f.
Lemma env_finite: forall rho, finite_idfun (env_get rho).
intros.