case neg hn =>
  unfold bitwise; simp [hm, hn]
  rw [←Nat.mul_two, Nat.pow_succ]
  have : m/2 < 2^k := (Nat.div_lt_iff_lt_mul (Nat.zero_lt_succ 1)).mpr hmk
  have : n/2 < 2^k := (Nat.div_lt_iff_lt_mul (Nat.zero_lt_succ 1)).mpr hnk
  cases f (m%2=1) (n%2=1) <;> simp
  . apply Nat.mul_lt_mul_of_pos_right ?_ (Nat.zero_lt_succ 1)
    exact h_ind ‹_› ‹_›
  . calc
    bitwise f (m/2) (n/2) * 2 + 1 
      < bitwise f (m/2) (n/2) * 2 + 2 := Nat.lt_succ_self _
    _ = (bitwise f (m/2) (n/2)) * 2 + 1*2 := rfl
    _ = (bitwise f (m/2) (n/2) + 1) * 2 := (Nat.add_mul _ _ 2).symm
    _ ≤ 2^k * 2 := Nat.mul_le_mul_right 2 (h_ind ‹m/2 < 2^k› ‹n/2 < 2^k›)
f : Bool → Bool → Bool
k : Nat
h_ind : ∀ {m n : Nat}, m < 2 ^ k → n < 2 ^ k → bitwise f m n < 2 ^ k
m n : Nat
hmk : m < 2 ^ succ k
hnk : n < 2 ^ succ k
hm : ¬m = 0
hn : ¬n = 0
⊢ bitwise f m n < 2 ^ succ k
no goals