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

Lemma equiv_star_lam s t : lam t -> s ≡ t <-> s ≻* t.