∀ {R : Type u_1} {n : Type u_2} [inst : CommSemiring R] [inst_1 : Fintype n] [inst_2 : DecidableEq n] {M : Type u_4}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : CoalgebraStruct R M],
  CoalgebraStruct.counit ∘ₗ Finsupp.lcoeFun = CoalgebraStruct.counit