∀ (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
          (TensorProduct.lcurry (RingHom.id R) N P (TensorProduct R M (TensorProduct R N P)) ∘ₗ
            TensorProduct.mk R M (TensorProduct R N P))) ∘ₗ
      TensorProduct.lift
        (TensorProduct.uncurry (RingHom.id R) N P (TensorProduct R (TensorProduct R M N) P) ∘ₗ
          TensorProduct.curry (TensorProduct.mk R (TensorProduct R M N) P)) =
    LinearMap.id