Affine.Triangle.excenterExists
∀ {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] (t : Affine.Triangle ℝ P) (signs : Finset (Fin 3)),
Affine.Simplex.ExcenterExists t signsAll excenters exist for a triangle.
- 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.
Cites12
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
- Compl.complproof · cited by 2,925
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Affine.Trianglestatement and proof · cited by 75
- Affine.Simplex.ExcenterExistsstatement · cited by 53
- Affine.Simplex.excenterExists_emptyproof · cited by 28
- Affine.Simplex.excenterExists_singletonproof · cited by 13
- Affine.Simplex.excenterExists_complproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Triangle.affineSpan_pair_eq_orthRadiusproof · cited by 1
- Affine.Triangle.two_zsmul_oangle_excenter_eqproof · cited by 0