dsimp
f : Bool → Bool → Bool
m n : Nat
hm : ¬m = 0
⊢ (if n = 0 then if flip f true false = true then m else 0
    else
      let n' := m / 2;
      let m' := n / 2;
      let b₁ := m % 2 = 1;
      let b₂ := n % 2 = 1;
      let r := bitwise (flip f) n' m';
      if flip f (decide b₁) (decide b₂) = true then r + r + 1 else r + r) =
    if n = 0 then if f false true = true then m else 0
    else
      let n' := n / 2;
      let m' := m / 2;
      let b₁ := n % 2 = 1;
      let b₂ := m % 2 = 1;
      let r := bitwise f n' m';
      if f (decide b₁) (decide b₂) = true then r + r + 1 else r + r
f : Bool → Bool → Bool
m n : Nat
hm : ¬m = 0
⊢ (if n = 0 then if flip f true false = true then m else 0
    else
      if flip f (decide (m % 2 = 1)) (decide (n % 2 = 1)) = true then
        bitwise (flip f) (m / 2) (n / 2) + bitwise (flip f) (m / 2) (n / 2) + 1
      else bitwise (flip f) (m / 2) (n / 2) + bitwise (flip f) (m / 2) (n / 2)) =
    if n = 0 then if f false true = true then m else 0
    else
      if f (decide (n % 2 = 1)) (decide (m % 2 = 1)) = true then
        bitwise f (n / 2) (m / 2) + bitwise f (n / 2) (m / 2) + 1
      else bitwise f (n / 2) (m / 2) + bitwise f (n / 2) (m / 2)