∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : HopfAlgebra R A] (a : A),
  (LinearMap.mul' R A) ((LinearMap.rTensor A (HopfAlgebraStruct.antipode R)) (CoalgebraStruct.comul a)) =
    (algebraMap R A) (CoalgebraStruct.counit a)