simp only [Nat.one_add, Nat.add_one, Nat.succ_add, Nat.add_succ,
  add_zero, propagateCarry2, zero_add]
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'
x : β → ℕ → Bool
init_carry : α → Bool
next_carry : (α → Bool) → (β → Bool) → α → Bool
n i : ℕ
⊢ (next_carry (propagateCarry2 init_carry next_carry x (i + n)) fun i_1 => x i_1 (i + n)) =
    propagateCarry2 init_carry next_carry x (i + (1 + n))
no goals