∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {X : Type u_3} [inst_4 : TopologicalSpace X] {c x : X → P} {R : X → ℝ} {a₀ : X}
  {s : Set X},
  ContinuousWithinAt c s a₀ →
    ContinuousWithinAt R s a₀ →
      ContinuousWithinAt x s a₀ →
        x a₀ ≠ c a₀ → ContinuousWithinAt (fun a => EuclideanGeometry.inversion (c a) (R a) (x a)) s a₀