∀ {R : Type u_1} [inst : Ring R] {S : Type u_2} [inst_1 : Ring S] (I : Ideal R) (J : Ideal S) [inst_2 : I.IsTwoSided]
  [inst_3 : J.IsTwoSided] (f : R ≃+* S) (hIJ : J = Ideal.map (↑f) I),
  Function.LeftInverse (⇑(Ideal.quotientMap I ↑f.symm ⋯)) (↑↑(Ideal.quotientMap J ↑f ⋯)).toFun