induction k generalizing n
k n : Nat
⊢ n &&& 2 ^ k - 1 = n % 2 ^ k
case zero
n : Nat
⊢ n &&& 2 ^ zero - 1 = n % 2 ^ zero

case succ
n✝ : Nat
n_ih✝ : ∀ (n : Nat), n &&& 2 ^ n✝ - 1 = n % 2 ^ n✝
n : Nat
⊢ n &&& 2 ^ succ n✝ - 1 = n % 2 ^ succ n✝