simp
case refl
f : Bool → Bool → Bool
f_stable : f false false = false
n : Nat
⊢ (if 0 = 0 then if f false true = true then n else 0
      else
        if n = 0 then if f true false = true then 0 else 0
        else
          let n' := 0 / 2;
          let m' := n / 2;
          let b₁ := 0 % 2 = 1;
          let b₂ := n % 2 = 1;
          let r := bitwise f n' m';
          if f (decide b₁) (decide b₂) = true then r + r + 1 else r + r) %
      2 =
    if f (decide (0 % 2 = 1)) (decide (n % 2 = 1)) = true then 1 else 0
case refl
f : Bool → Bool → Bool
f_stable : f false false = false
n : Nat
⊢ (if f false true = true then n else 0) % 2 = if f false (decide (n % 2 = 1)) = true then 1 else 0