∀ {ι : Type w} {R : Type u} [inst : Semiring R] [Nontrivial R] {M : Type v} [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] {v : ι → M} (i : LinearIndependent R v),
  i.Maximal ↔ ∀ (κ : Type v) (w : κ → M), LinearIndependent R w → ∀ (j : ι → κ), w ∘ j = v → Function.Surjective j