Tree Induction Consider the definition of binary trees given in the lectures data Tree a - Nul I Node (Tree a) a (Tree a) and the following three functions f :: Tree a -> Int f (Node Nul x Nul) -1 f (Node l x r )- (f 1) + (f r) F1 F2 F3 g :: Tree a - Int h :: Int -> Tree a -> Int h acc Nul - acc h acc (Node Nul x Nul)acc 1 h acc (Node 1 x r h (h acc1) r H1 H2 H3 Establish, using structural induction, that f t g t for all trees t of type Tree a State clearly what property P is being proved by induction, including any quantifiers needed in the statement of P and in the inductive hypothesis. Tree Induction Consider the definition of binary trees given in the lectures data Tree a - Nul I Node (Tree a) a (Tree a) and the following three functions f :: Tree a -> Int f (Node Nul x Nul) -1 f (Node l x r )- (f 1) + (f r) F1 F2 F3 g :: Tree a - Int h :: Int -> Tree a -> Int h acc Nul - acc h acc (Node Nul x Nul)acc 1 h acc (Node 1 x r h (h acc1) r H1 H2 H3 Establish, using structural induction, that f t g t for all trees t of type Tree a State clearly what property P is being proved by induction, including any quantifiers needed in the statement of P and in the inductive hypothesis