∀ (R : Type u_1) [inst : Semiring R] (motive : (∃ n f, Function.Injective ⇑f) → Prop)
  (x : ∃ n f, Function.Injective ⇑f),
  (∀ (n : ℕ) (f : (Fin (n + 1) → R) →ₗ[R] Fin n → R) (inj : Function.Injective ⇑f), motive ⋯) → motive x