have := h₃ 0
case zero.succ.succ
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✝¹ n✝ : ℕ
h₁ :
  propagateCarry2 init_carry (fun carry bits => (next_bit carry bits).fst) seq₁ (Nat.succ n✝¹) =
    propagateCarry2 init_carry (fun carry bits => (next_bit carry bits).fst) seq₂ (Nat.succ n✝)
h₃ : ∀ (y : ℕ) (b : β), y ≤ Nat.zero → seq₁ b (Nat.succ n✝¹ + y) = seq₂ b (Nat.succ n✝ + y)
⊢ (next_bit (propagateCarry2 init_carry (fun carry bits => (next_bit carry bits).fst) seq₂ (Nat.succ n✝)) fun j =>
        seq₁ j (n✝¹ + 1)).snd =
    (next_bit (propagateCarry2 init_carry (fun c b => (next_bit c b).fst) seq₂ (n✝ + 1)) fun j => seq₂ j (n✝ + 1)).snd
case zero.succ.succ
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✝¹ n✝ : ℕ
h₁ :
  propagateCarry2 init_carry (fun carry bits => (next_bit carry bits).fst) seq₁ (Nat.succ n✝¹) =
    propagateCarry2 init_carry (fun carry bits => (next_bit carry bits).fst) seq₂ (Nat.succ n✝)
h₃ : ∀ (y : ℕ) (b : β), y ≤ Nat.zero → seq₁ b (Nat.succ n✝¹ + y) = seq₂ b (Nat.succ n✝ + y)
this : ∀ (b : β), 0 ≤ Nat.zero → seq₁ b (Nat.succ n✝¹ + 0) = seq₂ b (Nat.succ n✝ + 0)
⊢ (next_bit (propagateCarry2 init_carry (fun carry bits => (next_bit carry bits).fst) seq₂ (Nat.succ n✝)) fun j =>
        seq₁ j (n✝¹ + 1)).snd =
    (next_bit (propagateCarry2 init_carry (fun c b => (next_bit c b).fst) seq₂ (n✝ + 1)) fun j => seq₂ j (n✝ + 1)).snd