Affine.Simplex.ExcenterExists.excenter_eq_incenter_iff
∀ {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 → (s.excenter signs = s.incenter ↔ signs = ∅ ∨ signs = Finset.univ)- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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 and proof · cited by 13,712
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Affine.Simplexstatement and proof · cited by 471
- Affine.Simplex.excenterstatement and proof · cited by 63
- Affine.Simplex.ExcenterExistsstatement and proof · cited by 53
- Affine.Simplex.incenterstatement · cited by 35
- Affine.Simplex.excenterExists_emptyproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.excenter_singleton_ne_incenterproof · cited by 1