(* ----------------- 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_open : forall rho e e',
(forall v, lc_exp (nom_val_to_exp v)) ->
(nom_envsubst rho (open e e')) = (open (nom_envsubst rho e) (nom_envsubst rho e')).