(* Furthermore, we can also prove that closed values have no free variables after translation.  This proof is done by mutual induction on the closed_val/closed_env derivation. So before we can do that, we need to ask Coq to derive the appropriate induction scheme. *)

Lemma fv_closed_env :
(forall rho, closed_env rho -> forall e, fv_exp e [<=] dom_rho rho ->
fv_exp (nom_envsubst rho e) [=] {}).