∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (A : Type u_4)
  {B : Type u_5} {D : Type u_7} [inst_3 : CommRing A] [inst_4 : Algebra R A] [inst_5 : Algebra S A]
  [inst_6 : IsScalarTower R S A] [inst_7 : CommRing B] [inst_8 : Algebra R B] [inst_9 : CommRing D]
  [inst_10 : Algebra R D] {f : B →ₐ[R] D}, f.Flat → (Algebra.TensorProduct.lTensor A f).Flat