∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] {a : A},
  IsGroupLikeElem R a → (HopfAlgebraStruct.antipode R) ((HopfAlgebraStruct.antipode R) a) = a