Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_pair
∀ {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]
{signs : Finset (Fin (n + 1))},
s.ExcenterExists signs → ∀ (i j : Fin (n + 1)), s.excenter signs ∉ line[ℝ, s.points i, s.points j]- 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.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Moduleproof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement and proof · cited by 13,712
- AddCommGroupproof · cited by 12,871
- Ringproof · cited by 7,463
- Set.imageproof · cited by 5,609
- Set.rangeproof · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- AddTorsorproof · cited by 1,657
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.incenter_notMem_affineSpan_pairproof · cited by 0