(Haskell) Assume that the lists are finite and the functions all terminate. Consider the following functions:

(.)::(b + c)(a + b)(a + c) 9.f = 1 + g(f) map : (a + b) + ([a] [b]) map f l = 1 map f (x : xs) = (f a) : (map f xs) Prove that map (f.g) xs = map f (map g xs) where xs is any list. (.)::(b + c)(a + b)(a + c) 9.f = 1 + g(f) map : (a + b) + ([a] [b]) map f l = 1 map f (x : xs) = (f a) : (map f xs) Prove that map (f.g) xs = map f (map g xs) where xs is any list