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

Theorem beta_whnf : forall (e : env) (t : term), sn (ctxt beta) e t -> {u : term | red beta e t u & head_normal beta e u}.