(* Higher Order *)

Definition normalizing {X:Type} (R:relation X) :=
  forall t, exists t',
    (multi R) t t' /\ normal_form R t'.

(* Specifications: *)
Lemma multistep_congr_1 : forall t1 t1' t2, t1 ===>* t1' -> P t1 t2 ===>* P t1' t2.