∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : IsDedekindDomain A] {I : Ideal R}
  {J : Ideal A} [inst_3 : IsDedekindDomain R] (f : R ⧸ I ≃+* A ⧸ J) (hI : I ≠ ⊥) (hJ : J ≠ ⊥),
  normalizedFactorsEquivOfQuotEquiv f hI hJ =
    { toFun := fun j => ⟨↑((idealFactorsEquivOfQuotEquiv f) ⟨↑j, ⋯⟩), ⋯⟩,
      invFun := fun j => ⟨↑((idealFactorsEquivOfQuotEquiv f).symm ⟨↑j, ⋯⟩), ⋯⟩, left_inv := ⋯, right_inv := ⋯ }