Proof using.
intros.
induction H.
- simpl. rewrite <- app_nil_r. econstructor; eauto. constructor.
- concludes. rewrite app_ass.
econstructor; eauto.
Qed.

Lemma refl_trans_n1_1n_trace :
forall step x y l,
refl_trans_n1_trace step x y l ->
refl_trans_1n_trace step x y l.