Proof using.
intros.
apply clos_rt_rtn1_iff.
eapply rt_trans; apply clos_rt_rtn1_iff; eauto.
Qed.

Lemma dup_drop_step_star_step_n1 :
forall l l' l'',
dup_drop_step_star l l' ->
dup_drop_step l' l'' ->
dup_drop_step_star l l''.