Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter
∀ {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} {signs : Finset (Fin (n + 1))},
s.ExcenterExists signs →
∀ (i : Fin (n + 1)),
SignType.sign ((s.signedInfDist i) (s.excenter signs)) = SignType.sign (s.excenterWeights signs i)- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement and proof · cited by 13,712
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- OrderHomstatement · cited by 934
- VSub.vsubproof · cited by 817
- Affine.Simplexstatement and proof · cited by 471
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.sign_touchpointWeightsproof · cited by 4
- Affine.Simplex.sign_signedInfDist_incenterproof · cited by 0