Consider the definition of binary trees given in the lectures data Tree a= Nul | Node (Tree a) a (Tree a) and the following three functions: f:: Tree a -> Int f (Node Nul x Nul) = 1 F1 F2 F3 f (Node 1 x r ) (f 1) + (f r) 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 xr h (h acc 1) r -- H3 H1 H2 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 Consider the definition of binary trees given in the lectures data Tree a= Nul | Node (Tree a) a (Tree a) and the following three functions: f:: Tree a -> Int f (Node Nul x Nul) = 1 F1 F2 F3 f (Node 1 x r ) (f 1) + (f r) 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 xr h (h acc 1) r -- H3 H1 H2 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