∀ {R : Type u_2} {A : Type u_1} [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) (f_surj : Function.Surjective ⇑↑f)
  (fsym_surj : Function.Surjective ⇑↑f.symm),
  (↑(idealFactorsFunOfQuotHom f_surj)).comp ↑(idealFactorsFunOfQuotHom fsym_surj) = OrderHom.id