∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  (I : Ideal S) [IsAdicComplete I S] [inst_4 : CommRing A] [inst_5 : Algebra R A] {f g : A →ₐ[R] S},
  (∀ (n : ℕ), (Ideal.Quotient.mkₐ R (I ^ n)).comp f = (Ideal.Quotient.mkₐ R (I ^ n)).comp g) → f = g