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