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

Lemma beta_whnf_rec : forall (e : env) (t : term) (args : list term), sn (ctxt beta) e (app_list args t) -> {u : term | red beta e (app_list args t) u & head_normal beta e u}.