Using induction, I want to prove that $ A_0^{x-1}(1) = x $ for $ x > 0 $ where $$ A_m(n) = A(m, n) $$ and $$ A_m^k(n) = \underbrace{A_m(A_m(...A_m(n)...))}_\text{k A's} $$
After proving the base case, I assume that $ A_0^{n-1}(1) = n $ is true. My inductive hypothesis is $$ A_0^{(n+1)-1}(1) = n + 1 $$
Is this correct?