Theorems · Theorem · geometry

EuclideanGeometry.preimage_inversion_perpBisector_inversion

∀ {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 ⁻¹' ↑(AffineSubspace.perpBisector c (EuclideanGeometry.inversion c R y)) =
        Metric.sphere y (dist y c) \ {c}

Defined in

Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane

Cited by

1 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor