∀ {R : Type u_1} [inst : Semiring R] (x x_1 : ℕ) (x_2 : (Fin x → R) →ₗ[R] Fin x_1 → R)
  (motive : (∃ h, x_2 ∘ₗ h = LinearMap.id) → Prop) (x_3 : ∃ h, x_2 ∘ₗ h = LinearMap.id),
  (∀ (w : (Fin x_1 → R) →ₗ[R] Fin x → R) (eq : x_2 ∘ₗ w = LinearMap.id), motive ⋯) → motive x_3