∀ {R : Type u_3} {A : Type u_1} {B : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid A] [inst_2 : Module R A]
  [inst_3 : AddCommMonoid B] [inst_4 : Module R B] [inst_5 : CoalgebraStruct R A] [inst_6 : CoalgebraStruct R B]
  (f : A →ₗc[R] B) (f' : A → B) (h : f' = ⇑f),
  TensorProduct.map ((↑f).copy f' h) ((↑f).copy f' h) ∘ₗ CoalgebraStruct.comul = CoalgebraStruct.comul ∘ₗ (↑f).copy f' h