∀ (R : Type u) (ι : Type v) (A : Type w) [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
  [inst_3 : CoalgebraStruct R A] (i : ι) (a : A), (CoalgebraStruct.counit fun₀ | i => a) = CoalgebraStruct.counit a