∀ {R₁ : Type u_1} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R₁] [inst_1 : Ring A] [inst_2 : Algebra R₁ A]
  [inst_3 : Semiring B] [inst_4 : Algebra R₁ B] (I : Ideal A) [inst_5 : I.IsTwoSided] (f f_1 : A →ₐ[R₁] B)
  (e_f : f = f_1) (hI : ∀ a ∈ I, f a = 0), Ideal.Quotient.liftₐ I f hI = Ideal.Quotient.liftₐ I f_1 ⋯