Admitted. (* 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.