(* ----------------- nom_envsubst reductions ------------------- *)
(* We can think of a an environment as a multi-substitution for locally nameless terms.  Therefore, the nom_envsubst function inherits many of the properties of the subst_exp function.  *)

Lemma nom_envsubst_var : forall x rho e rho',
closed_env rho ->
Some (e,rho') = rho_lookup x rho ->
nom_envsubst rho (var_f x) = nom_envsubst rho' (nom_to_exp e).