∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
  {ι : Type u_2} (v : ι → M),
  LinearIndependent R v → ∀ (w : Set M) [Finite ↑w], Set.range v ≤ ↑(Submodule.span R w) → Finite ι