simp [h₁]
case zero.succ.zero
α β α' β' : Type
γ : β → Type
init_carry : α → Bool
next_carry : (α → Bool) → (β → Bool) → α → Bool
next_bit : (α → Bool) → (β → Bool) → (α → Bool) × Bool
inst✝¹ : Fintype α
inst✝ : Fintype α'
seq₁ seq₂ : β → ℕ → Bool
n✝ : ℕ
h₁ :
  (next_bit (propagateCarry2 init_carry (fun carry bits => (next_bit carry bits).fst) seq₁ n✝) fun i => seq₁ i n✝).fst =
    init_carry
h₃ : ∀ (y : ℕ) (b : β), y = 0 → seq₁ b (Nat.succ n✝ + y) = seq₂ b y
this : ∀ (i : β), seq₁ i (n✝ + 1) = seq₂ i 0
⊢ (next_bit (next_bit (propagateCarry2 init_carry (fun c b => (next_bit c b).fst) seq₁ n✝) fun i => seq₁ i n✝).fst
        fun j => seq₂ j 0).snd =
    (next_bit init_carry fun j => seq₂ j 0).snd
no goals