∀ {R : Type u} {M : Type v} {N : Type u_1} {P : Type u_2} {Q : Type u_3} [inst : CommSemiring R]
  [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [inst_3 : AddCommMonoid N] [inst_4 : Module R N]
  [inst_5 : AddCommMonoid P] [inst_6 : Module R P] [inst_7 : AddCommMonoid Q] [inst_8 : Module R Q] {f : N →ₗ[R] P},
  Function.Injective ⇑f →
    ∀ (e : P ≃ₗ[R] Q),
      Function.Injective ⇑(LinearMap.rTensor M f) ↔ Function.Injective ⇑(LinearMap.rTensor M (↑e ∘ₗ f).range.subtype)