Problem 7. (30 points) Make sure you read Chapter 16 before attempting this problem.] Chapter 16. Exercise 6, page 247. This problem has two parts. Given the following data type data Tree = Leaf Int | Node Tree Tree 1. (5+5 10) First define functions that count the number of leaves (leaves) and the number of internal nodes (nodes) in a tree. The function types are as follows. leaves :: Tree -> Int nodes: Tree ->Int 2. (Base case 10 points +inductive case 10 points) Prove the following property by induction on trees leaves t nodes t + 1 Problem 7. (30 points) Make sure you read Chapter 16 before attempting this problem.] Chapter 16. Exercise 6, page 247. This problem has two parts. Given the following data type data Tree = Leaf Int | Node Tree Tree 1. (5+5 10) First define functions that count the number of leaves (leaves) and the number of internal nodes (nodes) in a tree. The function types are as follows. leaves :: Tree -> Int nodes: Tree ->Int 2. (Base case 10 points +inductive case 10 points) Prove the following property by induction on trees leaves t nodes t + 1