unfold sn, transp in |- *.
simple induction 1; intros.
apply Acc_intro; intros.
elim commut_subterm_R_exp with (e, x) (f, u) (f, y); intros; auto with pts.
inversion_clear H4 in H5.
apply H1 with y0; auto with pts.
Qed.
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).