Definition ord_conv : relation (value * value) :=
    clos_trans (value * value) (swapprod value ord_norm1).

(* Specifications: *)
Lemma ord_cv_no_swap : forall (e : env) (u ru : term), red R e ru u -> forall v rv : term, red R e rv v -> forall su sv : value, ord_norm1 (e, ru) su -> ord_norm1 (e, rv) sv -> ord_conv (e, u, (e, v)) (su, sv).
Lemma ord_cv_swap : forall (e : env) (u ru : term), red R e ru u -> forall v rv : term, red R e rv v -> forall su sv : value, ord_norm1 (e, ru) su -> ord_norm1 (e, rv) sv -> ord_conv (e, u, (e, v)) (sv, su).
Lemma sn_acc_ord_conv : forall (e : env) (u v : term), sn (ctxt R) e u -> sn (ctxt R) e v -> Acc ord_conv (e, u, (e, v)).