∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {E : Type u_3} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E] {f₀ f₁ : E → F}
  {s : Set E} {x v : E},
  f₀ =ᶠ[nhdsWithin x s] f₁ →
    f₀ x = f₁ x → (LineDifferentiableWithinAt 𝕜 f₀ s x v ↔ LineDifferentiableWithinAt 𝕜 f₁ s x v)