Discrete math question

(4 points) Let A be a variation of the Ackermann function defined by 2n if m = 0 A(m, n) = 0 if m > 1 and n = 0 2 if m > 1 and n = 1 A(m - 1, A(m, n - 1)) if m > 1 and n > 2 Use (regular linear) induction to prove that A(1, n) = 2" for all positive integers n