unfold bitwise
case refl
f : Bool → Bool → Bool
k : Nat
h_ind : ∀ {m n : Nat}, m < 2 ^ k → n < 2 ^ k → bitwise f m n < 2 ^ k
m : Nat
hmk : m < 2 ^ succ k
hm : ¬m = 0
hnk : 0 < 2 ^ succ k
⊢ bitwise f m 0 < 2 ^ succ k
case refl
f : Bool → Bool → Bool
k : Nat
h_ind : ∀ {m n : Nat}, m < 2 ^ k → n < 2 ^ k → bitwise f m n < 2 ^ k
m : Nat
hmk : m < 2 ^ succ k
hm : ¬m = 0
hnk : 0 < 2 ^ succ k
⊢ (if m = 0 then if f false true = true then 0 else 0
    else
      if 0 = 0 then if f true false = true then m else 0
      else
        let n' := m / 2;
        let m' := 0 / 2;
        let b₁ := m % 2 = 1;
        let b₂ := 0 % 2 = 1;
        let r := bitwise f n' m';
        if f (decide b₁) (decide b₂) = true then r + r + 1 else r + r) <
    2 ^ succ k