Definition whnf_bd_ord (x y : approx) :=
    lexprod value (fun _ : value => value) (R_exp beta_delta)
      (fun _ : value => subterm) (f1 x) (f1 y).

Lemma bd_app_list_ctxt : forall (l : list term) (e : env) (u v : term), ctxt beta_delta e u v -> ctxt beta_delta e (app_list l u) (app_list l v).