rw [Nat.mul_sub_div 0 2 (2^k) (by rw [Nat.mul_comm]; exact Nat.pos_pow_of_pos (n:=2) (k+1) (by decide))]
case hdiv
k : Nat
h_ind : ∀ (n : Nat), n &&& 2 ^ k - 1 = n % 2 ^ k
n : Nat
⊢ bitwise and (n / 2) ((2 * 2 ^ k - 1) / 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) / 2