∀ {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] {c y : P} {R : ℝ},
  R ≠ 0 →
    y ≠ c →
      EuclideanGeometry.inversion c R '' Metric.sphere y (dist y c) =
        insert c ↑(AffineSubspace.perpBisector c (EuclideanGeometry.inversion c R y))