∀ {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]
  (f : Derivation R A ↥I) (x y : A),
  ((Submodule.restrictScalars R I).subtype ∘ₗ ↑f + (IsScalarTower.toAlgHom R A B).toLinearMap).toFun (x + y) =
    ((Submodule.restrictScalars R I).subtype ∘ₗ ↑f + (IsScalarTower.toAlgHom R A B).toLinearMap).toFun x +
      ((Submodule.restrictScalars R I).subtype ∘ₗ ↑f + (IsScalarTower.toAlgHom R A B).toLinearMap).toFun y