induction' n using Nat.two_step_induction with n h1 h2
n : ℕ
⊢ a n = 2 ^ n + 3 ^ n
case H1

⊢ a 0 = 2 ^ 0 + 3 ^ 0

case H2

⊢ a 1 = 2 ^ 1 + 3 ^ 1

case H3
n : ℕ
h1 : a n = 2 ^ n + 3 ^ n
h2 : a (Nat.succ n) = 2 ^ Nat.succ n + 3 ^ Nat.succ n
⊢ a (Nat.succ (Nat.succ n)) = 2 ^ Nat.succ (Nat.succ n) + 3 ^ Nat.succ (Nat.succ n)