explain

d) Program Verification in Haskell: Consider the following definitions: (++)::[a][a][]++ys(x:xs)++ys[a]=ys=x:(xs++ys) f:::[a][a]f[]=[]f(x:xs)=fxs++[x,x] Prove by induction on lists xs that f(xs+ys)=fys+fxs. In the proof you may use that following laws hold for all finite lists x and ys. (1) (xs++ys)++zs=xs++(ys++zs) (2) xs++[]=xs