∀ (R : Type u_2) {A : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
  [inst_3 : Coalgebra R A] (a : A),
  IsGroupLikeElem R a = (CoalgebraStruct.counit a = 1 ∧ CoalgebraStruct.comul a = a ⊗ₜ[R] a)