An Inductive Proof of the Correctness of foo

• Base Case: foo squares argument 0, because when given 0 foo returns 0, and the square of 0 is 0.

• Induction Hypothesis (IH): Assume that foo squares n-1.

• Inductive Step:
  1. (foo n) returns foo applied to n-1 plus 2n-1 (by inspection of foo and elementary algebra)

  2. foo applied to n-1 is (n-1)² (by the IH)

  3. (n-1)² = n² - 2n + 1 (by elementary algebra)