∀ {R : Type u} {M : Type v} {M₂ : Type w} {M₃ : Type y} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid M₂] [inst_3 : AddCommMonoid M₃] [inst_4 : Module R M] [inst_5 : Module R M₂]
  [inst_6 : Module R M₃] (f : M × M₂ →ₗ[R] M₃), (f ∘ₗ LinearMap.inl R M M₂).coprod (f ∘ₗ LinearMap.inr R M M₂) = f