∀ {R : Type u_1} {S : Type u_2} {N : Type u_4} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] {A : Subalgebra R S},
  A.FG →
    ∀ {t t' : TensorProduct R (↥A) N},
      (LinearMap.rTensor N A.val.toLinearMap) t = (LinearMap.rTensor N A.val.toLinearMap) t' →
        ∃ B,
          ∃ (hAB : A ≤ B),
            B.FG ∧
              (LinearMap.rTensor N (Subalgebra.inclusion hAB).toLinearMap) t =
                (LinearMap.rTensor N (Subalgebra.inclusion hAB).toLinearMap) t'