∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
  [inst_3 : Coalgebra R A],
  TensorProduct.lift (LinearMap.lsmul R A ∘ₗ CoalgebraStruct.counit) ∘ₗ CoalgebraStruct.comul = LinearMap.id