Proof using.
intros.
induction H.
- constructor.
- eapply RTn1_step; eauto.
Qed.

Lemma RT1n_step :
forall (step : step_relation) x y z l l',
refl_trans_1n_trace step x y l ->
step y z l' ->
refl_trans_1n_trace step x z (l ++ l').