Hint Rewrite @app_nil_l @app_nil_r : sublist.

Lemma Zskipn_firstn: forall {A} n m (xs: list A),
0 <= n ->
skipn (Z.to_nat n) (firstn (Z.to_nat m) xs) =
firstn (Z.to_nat (m-n)) (skipn (Z.to_nat n) xs).