induction k generalizing i
k i : Nat
⊢ getBit (2 ^ k - 1) i = decide (i < k)
case zero
i : Nat
⊢ getBit (2 ^ zero - 1) i = decide (i < zero)

case succ
n✝ : Nat
n_ih✝ : ∀ (i : Nat), getBit (2 ^ n✝ - 1) i = decide (i < n✝)
i : Nat
⊢ getBit (2 ^ succ n✝ - 1) i = decide (i < succ n✝)