Affine.Simplex.sOppSide_point_excenter_singleton
∀ {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) [n.AtLeastTwo]
(i : Fin (n + 1)), (affineSpan ℝ (Set.range (s.faceOpposite i).points)).SOppSide (s.points i) (s.excenter {i})- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement · cited by 13,712
- Set.rangestatement · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Affine.Simplexstatement and proof · cited by 471
- affineSpanstatement · cited by 417
- Nat.AtLeastTwostatement and proof · cited by 405
- Affine.Simplex.pointsstatement · cited by 391
- SignTypeproof · cited by 318
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singletonproof · cited by 0