∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Nontrivial R]
  {ι : Type w} {v : ι → M},
  LinearIndependent R v → Cardinal.lift.{v, w} (Cardinal.mk ι) ≤ Cardinal.lift.{w, v} (Module.rank R M)