(* ----------------- 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_app : forall rho e1 e2,
nom_envsubst rho (app e1 e2) = app (nom_envsubst rho e1) (nom_envsubst rho e2).