∀ {R : Type u_3} {M : Type u_1} (A : Type u_2) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] (p : Submodule R M) (x : TensorProduct R A ↥p)
  (motive : x ∈ {t | ∃ m n, m ⊗ₜ[R] n = t} → Prop) (x_1 : x ∈ {t | ∃ m n, m ⊗ₜ[R] n = t}),
  (∀ (a : A) (m : ↥p) (h : a ⊗ₜ[R] m = x), motive ⋯) → motive x_1