{R : Type u_5} →
  [inst : CommSemiring R] →
    {A : Type u_6} →
      {B : Type u_7} →
        [inst_1 : AddCommMonoid A] →
          [inst_2 : AddCommMonoid B] →
            [inst_3 : Module R A] →
              [inst_4 : Module R B] →
                [inst_5 : CoalgebraStruct R A] →
                  [inst_6 : CoalgebraStruct R B] →
                    {motive : (A ≃ₗc[R] B) → Sort u} →
                      (t : A ≃ₗc[R] B) →
                        ((toCoalgHom : A →ₗc[R] B) →
                            (invFun : B → A) →
                              (left_inv : Function.LeftInverse invFun toCoalgHom.toFun) →
                                (right_inv : Function.RightInverse invFun toCoalgHom.toFun) →
                                  motive
                                    { toCoalgHom := toCoalgHom, invFun := invFun, left_inv := left_inv,
                                      right_inv := right_inv }) →
                          motive t