∀ (R : Type u_1) [inst : CommSemiring R] (p : ℕ) [hp : Fact (Nat.Prime p)] [inst_1 : CharP R p]
  (x x_1 : Ring.Perfection R p),
  ⟨fun n => (Perfection.coeff R p (n + 1)) (x + x_1), ⋯⟩ = ⟨fun n => (Perfection.coeff R p (n + 1)) (x + x_1), ⋯⟩