∀ (R : Type u_4) {M : Type u_2} [inst : TopologicalSpace M] {M₂ : Type u_3} [inst_1 : TopologicalSpace M₂]
  [inst_2 : Semiring R] [inst_3 : AddCommMonoid M] [inst_4 : AddCommMonoid M₂] [inst_5 : ContinuousAdd M]
  [inst_6 : Module R M] [inst_7 : ContinuousAdd M₂] [inst_8 : Module R M₂] (α : Type u_1) [inst_9 : TopologicalSpace α]
  (g : M →L[R] M₂) (x y : C(α, M)),
  (↑(AddMonoidHom.compLeftContinuous α (↑g).toAddMonoidHom ⋯)).toFun (x + y) =
    (↑(AddMonoidHom.compLeftContinuous α (↑g).toAddMonoidHom ⋯)).toFun x +
      (↑(AddMonoidHom.compLeftContinuous α (↑g).toAddMonoidHom ⋯)).toFun y