Admitted. (* Existential *)
Definition step_normal_form := normal_form step.
Definition normal_form_of (t t' : tm) :=
(t ===>* t' /\ step_normal_form t').
(** We have already seen that, for our language, single-step reduction is deterministic -- i.e., a given term can take a single step in at most one way.  It follows from this that, if [t] can reach a normal form, then this normal form is unique.  In other words, we can actually pronounce [normal_form t t'] as "[t'] is _the_ normal form of [t]." *)

(* Specifications: *)
Theorem normal_forms_unique:
deterministic normal_form_of.