∀ {R : Type u_2} {A : Type u_3} {B : Type u_1} [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 f₂ : A →ₐ[R] B),
  (Ideal.Quotient.mkₐ R I).comp f₁ = (Ideal.Quotient.mkₐ R I).comp f₂ →
    ∀ (x : A), (f₁.toLinearMap - f₂.toLinearMap) x ∈ Submodule.restrictScalars R I