∀ {ι : Type u'} {R : Type u_2} {K : Type u_3} {M : Type u_4} {v : ι → M} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : Semiring K] [inst_4 : SMulWithZero R K] [inst_5 : Module K M] [IsScalarTower R K M],
  (Function.Injective fun r => r • 1) → LinearIndependent K v → LinearIndependent R v