∀ {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) [inst_3 : IsAdicComplete I S] [inst_4 : CommRing A] [inst_5 : Algebra R A]
  (f : (n : ℕ) → A →ₐ[R] S ⧸ I ^ n) (hf : ∀ {m n : ℕ} (hle : m ≤ n), (Ideal.Quotient.factorₐ R ⋯).comp (f n) = f m),
  IsAdicComplete.liftAlgHom I f hf =
    (AlgHom.restrictScalars R ↑(AdicCompletion.ofAlgEquiv I).symm).comp (AdicCompletion.liftAlgHom I f ⋯)