Suppose we define good points using the following inductive definition:

Foundation: (3 , 1) is a good point Constructor: If (a , b) and (c , d) are good points, then so are (b 1, a + 1) and (a c + 1, b + d 1) Use structural induction to prove that a + b is even for every good point (a , b).

Part a) (1 pt) List the good points that can be created with one application of the constructor rule.

Part b) (1 pt) What is P(n) (i.e., predicate you are proving holds true for all natural numbers n)?

Part c) (2 pts) Base case:

Part d) (6 pts) Inductive step: