induction i generalizing k
k i : Nat
⊢ getBit (2 ^ k) i = decide (k = i)
case zero
k : Nat
⊢ getBit (2 ^ k) zero = decide (k = zero)

case succ
n✝ : Nat
n_ih✝ : ∀ (k : Nat), getBit (2 ^ k) n✝ = decide (k = n✝)
k : Nat
⊢ getBit (2 ^ k) (succ n✝) = decide (k = succ n✝)