Theorems · Theorem · geometry

AffineSubspace.signedInfDist_apply_of_mem

∀ {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}, x ∈ s → (s.signedInfDist p) x = 0

Defined in

Mathlib.Geometry.Euclidean.SignedDist

Cited by

2 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection