Proof with eauto.
intros s s' H.
induction H; intros ? ??...
- eapply eqTrans. eapply eqStep. eapply stepAppL. eassumption.
induction H0...
- induction H...
Qed.

(* Specifications: *)
Lemma equiv_star_lam s t : lam t -> s ≡ t <-> s ≻* t.
Lemma unique_normal_forms (s t : term) : lam s -> lam t ->  s ≡ t -> s = t.
Lemma evaluates_equiv s t : s ▷ t <-> s ≡ t /\ lam t.
Proof with eauto using star_equiv, evaluates_abst.