∀ (R : Type u_1) (S : Type u_2) (A : Type u_3) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
  [inst_3 : Semiring A] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [inst_6 : IsScalarTower R S A] (B : Type u_6)
  (C : Type u_7) [inst_7 : Semiring B] [inst_8 : Semiring C] [inst_9 : Algebra R B] [inst_10 : Algebra R C] (a : A)
  (x : B × C), ((Algebra.TensorProduct.prodRight R S A B C) (a ⊗ₜ[R] x)).2 = a ⊗ₜ[R] x.2