(* Need the mutual induction scheme for the next lemma! *)
Scheme nom_val_ind' := Induction for nom_val Sort Prop
 with  nom_env_ind' := Induction for nom_env Sort Prop.Combined Scheme nom_mutual from nom_val_ind', nom_env_ind'.

Lemma nom_soundness_val : forall v, bigstep (nom_val_to_exp v) (nom_val_to_exp v).