“…APPENDIX A PROOF OF LEMMA III.1The difference equation can be written from(17) as ∆y(k + 1) = f e (y(k), .., y(k − n y ))− f e (y(k − 1), .., y(k − n y − 1))(24) By adding and subtracting f e (y(k − 1), .., y(k − n y ))) ∆y(k + 1) = f e (y(k), .., y(k − n y )) − f e (y(k − 1),y(k − 1).., y(k − n y ))) + f e (y(k − 1), y(k − 1), .., y(k − n y ))) − f e (y(k − 1), .., y(k − n y − 1)) (25)From assumption A1 we have the f e differentiable. Further using differential mean value theorem (∂f e * /∂y(k) = f e (y(k), .)…”