Haskell - Prove by induction the following properties of map: map (f . g) = map f . map g map f...

Haskell - Prove by induction the following properties of map:

map (f . g) = map f . map g
map f . tail = tail . map f
map f . reverse = reverse . map f
map f . concat = concat . map (map f)
map f (xs ++ ys) = map f xs ++ map f ys