Proof using uii lmi rri.
intros.
pose proof lift_uniqueIndices_log net h; intuition.
find_copy_apply_lem_hyp lift_log_matching.
unfold log_matching, log_matching_nw in *.
intuition.
find_apply_lem_hyp exists_deghosted_packet.
break_exists.
intuition.
subst. destruct p; simpl in *; subst.
eapply_prop_hyp In In; simpl; eauto. intuition.
match goal with
| H : forall _ _ _, _ |- _ =>
specialize (H h e' e)
end; intuition.
repeat break_match. simpl in *. repeat find_rewrite. simpl in *.
intuition.
match goal with
| H : forall _, _ <= _ -> _ |- _ =>
specialize (H e'); conclude H ltac:(omega)
end. intuition.
eapply rachet; eauto.
Qed.

Lemma sorted_app_in_gt :
forall l1 l2 e e',
sorted (l1 ++ l2) ->
In e l1 ->
In e' l2 ->
eIndex e' < eIndex e.