(* ----------------- interpreter soundness for values ------------------- *)
(* The next step is to show that nominal values bigstep to themselves. In otherwords, we want to show that:  << Lemma nom_soundness_val : forall v, bigstep (nom_val_to_exp v) (nom_val_to_exp v). >>  To prove this lemma, we need to show that these nominal values translate LN values, and that these values are locally closed.  *)

(* Specifications: *)
Lemma nom_val_to_exp_is_value : forall v, is_value (nom_val_to_exp v).
Hint Resolve nom_val_to_exp_is_value.
Lemma nom_to_exp_lc : forall ne, lc_exp (nom_to_exp ne).
Scheme nom_val_ind' := Induction for nom_val Sort Prop
with  nom_env_ind' := Induction for nom_env Sort Prop.