Definition map_Znth i (L : A -> option (list B)) k := option_map (fun v => Znth i v) (L k).

Lemma map_incl_Znth : forall (m1 m2 : A -> option (list B)) i, map_incl m1 m2 -> map_incl (map_Znth i m1) (map_Znth i m2).