∀ (R : Type u_4) [inst : CommSemiring R] (M : Type u_1) (N : Type u_2) (P : Type u_3) [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : Module R M] [inst_5 : Module R N]
  [inst_6 : Module R P],
  TensorProduct.lift
        (TensorProduct.lift
          (↑LinearMap.lflip ∘ₗ (TensorProduct.mk R M P).compr₂ (TensorProduct.mk R (TensorProduct R M P) N))) ∘ₗ
      TensorProduct.lift
        (TensorProduct.lift
          (↑LinearMap.lflip ∘ₗ (TensorProduct.mk R M N).compr₂ (TensorProduct.mk R (TensorProduct R M N) P))) =
    LinearMap.id