by_cases m = 0
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
⊢ bitwise f m n < 2 ^ succ k
case pos
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
h✝ : m = 0
⊢ bitwise f m n < 2 ^ succ k

case neg
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
h✝ : ¬m = 0
⊢ bitwise f m n < 2 ^ succ k