∀ {a : ℝ} {l : Filter ℝ} {f f' g g' : ℝ → ℝ} {s : Set ℝ},
  Convex ℝ s →
    (∀ᶠ (x : ℝ) in nhdsWithin a (s \ {a}), HasDerivWithinAt f (f' x) (s \ {a}) x) →
      (∀ᶠ (x : ℝ) in nhdsWithin a (s \ {a}), HasDerivWithinAt g (g' x) (s \ {a}) x) →
        (∀ᶠ (x : ℝ) in nhdsWithin a (s \ {a}), g' x ≠ 0) →
          Filter.Tendsto f (nhdsWithin a (s \ {a})) (nhds 0) →
            Filter.Tendsto g (nhdsWithin a (s \ {a})) (nhds 0) →
              Filter.Tendsto (fun x => f' x / g' x) (nhdsWithin a (s \ {a})) l →
                Filter.Tendsto (fun x => f x / g x) (nhdsWithin a (s \ {a})) l