∀ {R : Type u_3} {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_2}
  [inst_3 : Fintype ι] (motive : (∃ f, LinearIndependent R f) → Prop) (x : ∃ f, LinearIndependent R f),
  (∀ (f : Fin (Fintype.card ι) → M) (hf : LinearIndependent R f), motive ⋯) → motive x