Theorems · Theorem · geometry

AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection

∀ {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] (s : AffineSubspace ℝ P) [inst_4 : Nonempty ↥s]
  [inst_5 : s.direction.HasOrthogonalProjection] (p : P) {x : P},
  (s.signedInfDist p) x =
    ((signedDist (p -ᵥ ↑((EuclideanGeometry.orthogonalProjection s) p)))
        ↑((EuclideanGeometry.orthogonalProjection s) x))
      x

Defined in

Mathlib.Geometry.Euclidean.SignedDist

Cited by

2 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection