∀ {R : Type u_3} {A : Type u_1} {B : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : Module R A] [inst_3 : SMulCommClass R A A] [inst_4 : IsScalarTower R A A]
  [inst_5 : NonUnitalNonAssocSemiring B] [inst_6 : Module R B] [inst_7 : SMulCommClass R B B]
  [inst_8 : IsScalarTower R B B] (a b c : TensorProduct R A B), (a + b) * c = a * c + b * c