Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range
∀ {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] {n : ℕ} [inst_4 : NeZero n] {s : Affine.Simplex ℝ P n} (i : Fin (n + 1)) {p : P},
p ∈ affineSpan ℝ (Set.range s.points) →
|(s.signedInfDist i) p| = dist p ↑((s.faceOpposite i).orthogonalProjectionSpan p)- Defined in
- Mathlib.Geometry.Euclidean.SignedDist
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Moduleproof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommGroupproof · cited by 12,871
- Ringproof · cited by 7,463
- Submodulestatement · cited by 7,192
- Set.imageproof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- Compl.complproof · cited by 2,925
Cited by3
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.dist_excenterproof · cited by 6