induction n using recBase2
n : Nat
⊢ recBase2 0 0 (fun x x_1 => x_1 + 1) n = log2 n
case zero

⊢ recBase2 0 0 (fun x x_1 => x_1 + 1) 0 = log2 0

case one

⊢ recBase2 0 0 (fun x x_1 => x_1 + 1) 1 = log2 1

case div2
n✝ : Nat
a✝ : recBase2 0 0 (fun x x_1 => x_1 + 1) (n✝ / 2 + 1) = log2 (n✝ / 2 + 1)
⊢ recBase2 0 0 (fun x x_1 => x_1 + 1) (n✝ + 2) = log2 (n✝ + 2)