induction k generalizing m n
f : Bool → Bool → Bool
m n k : Nat
hmk : m < 2 ^ k
hnk : n < 2 ^ k
⊢ bitwise f m n < 2 ^ k
case zero
f : Bool → Bool → Bool
m n : Nat
hmk : m < 2 ^ zero
hnk : n < 2 ^ zero
⊢ bitwise f m n < 2 ^ zero

case succ
f : Bool → Bool → Bool
n✝ : Nat
n_ih✝ : ∀ {m n : Nat}, m < 2 ^ n✝ → n < 2 ^ n✝ → bitwise f m n < 2 ^ n✝
m n : Nat
hmk : m < 2 ^ succ n✝
hnk : n < 2 ^ succ n✝
⊢ bitwise f m n < 2 ^ succ n✝