∀ {R : Type u_4} {M : Type u_1} {M₁ : Type u_2} {M₂ : Type u_3} [inst : Semiring R] [inst_1 : TopologicalSpace M]
  [inst_2 : TopologicalSpace M₁] [inst_3 : TopologicalSpace M₂] [inst_4 : AddCommMonoid M] [inst_5 : Module R M]
  [inst_6 : ContinuousAdd M] [inst_7 : AddCommMonoid M₁] [inst_8 : Module R M₁] [inst_9 : AddCommMonoid M₂]
  [inst_10 : Module R M₂] (f : (M₁ →L[R] M) × (M₂ →L[R] M)),
  (fun f => (f.comp (ContinuousLinearMap.inl R M₁ M₂), f.comp (ContinuousLinearMap.inr R M₁ M₂)))
      ((fun f => f.1.coprod f.2) f) =
    f