induction k generalizing n i
n k : Nat
hn : n < 2 ^ k
i : Nat
hi : i ≥ k
⊢ getBit n i = false
case zero
n : Nat
hn : n < 2 ^ zero
i : Nat
hi : i ≥ zero
⊢ getBit n i = false

case succ
n✝ : Nat
n_ih✝ : ∀ {n : Nat}, n < 2 ^ n✝ → ∀ (i : Nat), i ≥ n✝ → getBit n i = false
n : Nat
hn : n < 2 ^ succ n✝
i : Nat
hi : i ≥ succ n✝
⊢ getBit n i = false