(* Need the mutual induction scheme for the next lemma! *)
Combined Scheme nom_mutual from nom_val_ind', nom_env_ind'.

(* Specifications: *)
Lemma nom_val_to_exp_lc_mutual :
(forall v, lc_exp (nom_val_to_exp v)) /\
(forall rho, forall e, lc_exp e -> lc_exp (nom_envsubst rho e)).
Lemma nom_val_to_exp_lc : forall v,
lc_exp (nom_val_to_exp v).
Lemma nom_envsubst_lc : (forall rho, forall e, lc_exp e -> lc_exp (nom_envsubst rho e)).
eapply nom_val_to_exp_lc_mutual.