∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_5) {N : Type u_6} [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] (f : N →ₗ[R] R),
  ↑(TensorProduct.lid R M) ∘ₗ LinearMap.rTensor M f = TensorProduct.lift (LinearMap.lsmul R M ∘ₗ f)