Proof using A_eq_dec.
induction l; intros.
- destruct l'.
+ constructor.
+ simpl in *. exfalso. eauto.
- destruct (in_dec A_eq_dec a l').
+ eapply dup_drop_step_star_remove_In. auto.
apply IHl.
intros.
find_apply_lem_hyp remove_In_elim.
intuition.
find_apply_hyp_hyp.
simpl in *. intuition.
exfalso. eauto.
+ eapply dup_drop_step_star_step_1n.
eapply DDS_drop with (xs := []).
apply IHl.
simpl in *. intros.
find_copy_apply_hyp_hyp.
intuition.
subst. exfalso. eauto.
Qed.
End dup_drop_reorder.
Section step_failure_dup_drop_step.
Context `{params : FailureParams}.

(* Specifications: *)
Theorem step_failure_dup_drop_step :
forall ps ps' Sigma f,
dup_drop_step_star _ ps ps' ->
step_failure_star (f, mkNetwork ps Sigma) (f, mkNetwork ps' Sigma) [].