{R : Type u} →
  {A : Type v} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid A] →
        [inst_2 : Module R A] →
          [inst_3 : CoalgebraStruct R A] →
            {a : A} →
              {motive : Coalgebra.Repr R a → Sort u_2} →
                (t : Coalgebra.Repr R a) →
                  ({ι : Type u_1} →
                      (index : Finset ι) →
                        (left right : ι → A) →
                          (eq : ∑ i ∈ index, left i ⊗ₜ[R] right i = CoalgebraStruct.comul a) →
                            motive { ι := ι, index := index, left := left, right := right, eq := eq }) →
                    motive t