Give an inductive proof the fact that consecutively mapping two functions over a list is equivalent to mapping their composition over the list. That is: map f (map g xs) = map (f,g) xs The definitions of map and compose () are: map f [] = [] map f (x:xs) = f x : map f xs (f . g) x = f (gx) - M1 M2 a) State and prove the base case goal b) State the inductive hypothesis. c) State and prove the step case goal