Proof using.
intros.
find_copy_apply_lem_hyp reachable_sane.
find_copy_apply_lem_hyp reachable_seen.
find_copy_apply_lem_hyp reachable_equality.
break_exists.
match goal with H : step_dup _ _ _ |- _ => invcs H end.
- unfold seq_num_net_handlers in *.
match goal with
| [H : context [ if _ then _ else _ ] |- _] =>
revert H
end.
break_if; intros.
+ right. find_inversion. simpl in *.
unfold revertNetwork. simpl in *. intuition.
f_equal.
* f_equal. find_rewrite. symmetry.
match goal with
| |- filter ?f _ = filter ?g _ =>
assert (f = g) by
(apply functional_extensionality;
intros; repeat break_if; repeat find_rewrite; intuition)
end.
find_rewrite.
apply filter_dedup.
break_if; intuition.
* apply functional_extensionality.
intros. break_if; subst; intuition.
+ left. repeat break_let. find_inversion.
match goal with
| [ H : processPackets _ _ = _, H' : net_handlers _ _ _ _ = (_, d0, _) |- _ ] =>
eapply revertNetwork_deliver_step with (d := d0) in H; eauto
end.
break_exists.
break_and.
match goal with
| [H : nwPackets _ = _ |- _ ] =>
eapply (StepAsync_deliver _ _ _ _ H); eauto
end.
- left. unfold seq_num_input_handlers in *. repeat break_let.
find_inversion.
find_eapply_lem_hyp revertNetwork_input; eauto.
econstructor 2; simpl; eauto.
- right.
split; auto.
unfold revertNetwork.
f_equal. f_equal. f_equal.
simpl. find_rewrite. eauto using dedup_eliminates_duplicates.
Qed.

(* Specifications: *)
Lemma step_dup_star_revert_simulation :
forall net tr,
step_dup_star step_async_init net tr ->
exists tr', step_async_star step_async_init (revertNetwork net) tr' /\
filterMap trace_non_empty_out tr = filterMap trace_non_empty_out tr'.