Proof using.
intros.
apply clos_rt_rtn1_iff.
apply clos_rt_rt1n_iff.
econstructor; [eauto|].
apply clos_rt_rt1n_iff.
apply clos_rt_rtn1_iff.
auto.
Qed.

Lemma dup_drop_step_star_step_1 :
forall l l',
dup_drop_step l l' ->
dup_drop_step_star l l'.