Proof using.
intros.
induction H0.
- rewrite app_nil_r. rewrite <- app_nil_l.
econstructor.
constructor.
auto.
- concludes.
rewrite <- app_ass.
econstructor; eauto.
Qed.

Lemma refl_trans_1n_n1_trace :
forall step x y l,
refl_trans_1n_trace step x y l ->
refl_trans_n1_trace step x y l.