∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : CommRing B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (I : Ideal B) (f₁ f₁_1 : A →ₐ[R] B) (e_f₁ : f₁ = f₁_1)
  (f₂ f₂_1 : A →ₐ[R] B) (e_f₂ : f₂ = f₂_1) (e : (Ideal.Quotient.mkₐ R I).comp f₁ = (Ideal.Quotient.mkₐ R I).comp f₂),
  diffToIdealOfQuotientCompEq I f₁ f₂ e = diffToIdealOfQuotientCompEq I f₁_1 f₂_1 ⋯