(* ----------------- 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_fresh_eq : forall rho e,
closed_env rho ->
fv_exp e [=] {} ->
nom_envsubst rho e = e.