∀ {R : Type u_3} {A : Type u_2} {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) [inst_5 : Algebra A B] [inst_6 : IsScalarTower R A B],
  I ^ 2 = ⊥ →
    ∀ (f : A →ₐ[R] B) (e : (Ideal.Quotient.mkₐ R I).comp f = IsScalarTower.toAlgHom R A (B ⧸ I)) (x y : A),
      (diffToIdealOfQuotientCompEq I f (IsScalarTower.toAlgHom R A B) ⋯) (x * y) =
        x • (diffToIdealOfQuotientCompEq I f (IsScalarTower.toAlgHom R A B) ⋯) y +
          y • (diffToIdealOfQuotientCompEq I f (IsScalarTower.toAlgHom R A B) ⋯) x