∀ {R : Type u_3} [inst : CommRing R] {A : Type u_1} [inst_1 : AddCommGroup A] {B : Type u_2} [inst_2 : AddCommGroup B]
  [inst_3 : Module R A] [inst_4 : Module R B] (r : R) (c : CharacterModule (TensorProduct R A B)),
  { toFun := fun x => AddMonoidHom.comp (r • c) ↑((TensorProduct.mk R A B) x), map_add' := ⋯, map_smul' := ⋯ } =
    (RingHom.id R) r •
      { toFun := fun x => AddMonoidHom.comp c ↑((TensorProduct.mk R A B) x), map_add' := ⋯, map_smul' := ⋯ }