Corollary Zlength_upto : forall n, Zlength (upto n) = Z.of_nat n.

Lemma combine_upd_Znth : forall {A B} (l1 : list A) (l2 : list B) i x1 x2, 0 <= i < Zlength l1 -> Zlength l1 = Zlength l2 -> combine (upd_Znth i l1 x1) (upd_Znth i l2 x2) = upd_Znth i (combine l1 l2) (x1, x2).