Affine.Simplex.sign_signedInfDist_touchpoint_empty
∀ {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 j : Fin (n + 1)},
i ≠ j → SignType.sign ((s.signedInfDist j) (s.touchpoint ∅ i)) = SignType.sign ((s.signedInfDist j) s.incenter)- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement · cited by 13,712
- 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
- Affine.Simplexstatement and proof · cited by 471
- SignTypestatement · cited by 318
- ContinuousAffineMapstatement · cited by 263
- SignType.signstatement · cited by 128
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