Theorems · Theorem · geometry

AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert

∀ {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 x : P},
  x ∈ affineSpan ℝ (insert p ↑s) → |(s.signedInfDist p) x| = dist x ↑((EuclideanGeometry.orthogonalProjection s) x)

Defined in

Mathlib.Geometry.Euclidean.SignedDist

Cited by

1 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection