∀ (R₁ : Type u_1) {A : Type u_3} [inst : CommSemiring R₁] [inst_1 : Ring A] [inst_2 : Algebra R₁ A] {I J : Ideal A}
  [inst_3 : I.IsTwoSided] [inst_4 : J.IsTwoSided] (h : I = J) (x : A),
  (Ideal.quotientEquivAlgOfEq R₁ h) ((Ideal.Quotient.mk I) x) = (Ideal.Quotient.mk J) x