∀ {R : Type u_3} {M : Type u_2} {M₂ : Type u_1} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] (x y : M),
  (↑(LinearMap.applyₗ' R)).toFun (x + y) = (↑(LinearMap.applyₗ' R)).toFun x + (↑(LinearMap.applyₗ' R)).toFun y