Proof using.
induction 1; intros.
- auto.
- invc H.
+ simpl in *. intuition.
subst. auto.
+ apply IHclos_refl_trans_n1.
find_apply_lem_hyp in_app_or.
intuition.
Qed.

(* Specifications: *)
Lemma dup_drop_dup_early :
forall l l' a,
dup_drop_step_star l l' ->
In a l ->
dup_drop_step_star l (a :: l').