Affine.Simplex.ExcenterExists.exradius_pos
∀ {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 → 0 < s.exradius signs- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Affine.Simplexstatement and proof · cited by 471
- inv_ne_zeroproof · cited by 99
- Affine.Simplex.ExcenterExistsstatement and proof · cited by 53
- abs_posproof · cited by 45
- Affine.Simplex.exradiusstatement · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.touchpoint_injectiveproof · cited by 4
- Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadiusproof · cited by 2
- Affine.Simplex.inradius_posproof · cited by 0
- Affine.Simplex.exradius_singleton_posproof · cited by 0