∀ (R : Type u_1) (A : Type u_2) (M : Type u_3) (N : Type u_4) [inst : CommSemiring R] [inst_1 : CommSemiring A]
  [inst_2 : Algebra R A] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : AddCommMonoid N]
  [inst_6 : Module R N],
  LinearMap.tensorProduct R A M N =
    TensorProduct.AlgebraTensorModule.lift
      { toFun := fun a => a • LinearMap.baseChangeHom R A M N, map_add' := ⋯, map_smul' := ⋯ }