Haskell assignment (without imports)

1)

Given the following defenitions

(m1) map f [] = []

(m2) map f (x:xs) = f x : map f xs

(c1) [] ++ ys = ys

(c2) (x:xs) ++ ys = x : (xs ++ ys)

prove that for all lists xs and ys:

map f (xs ++ ys) = (map f xs) ++ (map f ys)