∀ (R : Type u_5) (S : Type u_6) (B : Type u_4) (M : Type u_1) (P : Type u_2) (Q : Type u_3) [inst : CommSemiring R]
  [inst_1 : Semiring B] [inst_2 : Algebra R B] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module B M]
  [inst_6 : IsScalarTower R B M] [inst_7 : AddCommMonoid P] [inst_8 : AddCommMonoid Q] [inst_9 : Module R Q]
  [inst_10 : CommSemiring S] [inst_11 : Module S M] [inst_12 : Module S P] [inst_13 : Algebra S B]
  [inst_14 : IsScalarTower S B M] [inst_15 : SMulCommClass R S M] [inst_16 : SMulCommClass S R M],
  TensorProduct.AlgebraTensorModule.lift
        (TensorProduct.AlgebraTensorModule.lift
          (↑LinearMap.lflip ∘ₗ
            (TensorProduct.AlgebraTensorModule.mk S B M P).compr₂
              (TensorProduct.AlgebraTensorModule.mk R B (TensorProduct S M P) Q))) ∘ₗ
      TensorProduct.AlgebraTensorModule.lift
        (TensorProduct.AlgebraTensorModule.lift
          (↑LinearMap.lflip ∘ₗ
            (TensorProduct.AlgebraTensorModule.mk R B M Q).compr₂
              (TensorProduct.AlgebraTensorModule.mk S B (TensorProduct R M Q) P))) =
    LinearMap.id