Given the following definitions in haskell:

(m1) map f [] = []

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

(c1) [] ++ ys = ys

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

prove for all lists xs and ys: map f (xs ++ ys) = (map f xs) ++ (map f ys).