Affine.Simplex.ExcenterExists.touchpoint_mem_exsphere
∀ {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)), s.touchpoint signs i ∈ s.exsphere signs- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 2 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.
Cites13
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
- EuclideanGeometry.Spherestatement · cited by 233
- Affine.Simplex.ExcenterExistsstatement and proof · cited by 53
- Affine.Simplex.touchpointstatement · cited by 49
- Affine.Simplex.exspherestatement · cited by 20
- EuclideanGeometry.mem_sphere'proof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_neproof · cited by 2
- Affine.Simplex.touchpoint_mem_insphereproof · cited by 0