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

Lemma map_Znth_add : forall (m1 m2 : A -> option (list B)) i, map_Znth i (map_add m1 m2) = map_add (map_Znth i m1) (map_Znth i m2).