Definition ord_norm1 : value -> value -> Prop := union value subterm R_exp.Definition ord_norm : value -> value -> Prop := clos_trans value ord_norm1.

(* Specifications: *)
Lemma ord_norm_intro : forall (e f : env) (x y z : term), subterm (f, y) (e, x) -> red R f y z -> ord_norm (f, z) (e, x).
Lemma sn_acc_ord_norm1 : forall (e : env) (t : term), sn (ctxt R) e t -> Acc ord_norm1 (e, t).