rw [Nat.mod_mul_div_left n 2 (2^k)]
case hdiv
k : Nat
h_ind : ∀ (n : Nat), n &&& 2 ^ k - 1 = n % 2 ^ k
n : Nat
⊢ bitwise and (n / 2) (2 ^ k - succ (0 / 2)) = n % (2 * 2 ^ k) / 2
case hdiv
k : Nat
h_ind : ∀ (n : Nat), n &&& 2 ^ k - 1 = n % 2 ^ k
n : Nat
⊢ bitwise and (n / 2) (2 ^ k - succ (0 / 2)) = n / 2 % 2 ^ k