Answer the question only with haskell code . get help from book : Discrete Math Using A Computer, Hall and O'Donnel

Exercise 5. Theorem proof

Theorem 1: max (length xs) (length (xs++ys)) = length (xs++ys)

Theorem 2: length (zip xs ys) = max (length xs) (length ys)

Theorem 3: length (xs ++ ys) = length xs + length ys

Using results of the above 2 theorems , prove theorem 3 below

Theorem 4: which states: length (zip xs (xs++ys)) = length xs + lenth ys