Affine.Simplex.ExcenterExists.touchpoint_injective
∀ {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 → Function.Injective (s.touchpoint signs)- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 4 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.
Cites51
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · 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
- SetLike.coeproof · cited by 8,199
- Ringproof · cited by 7,463
- Submoduleproof · cited by 7,192
- Set.imageproof · cited by 5,609
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
Cited by4
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_neproof · cited by 2
- Affine.Triangle.oangle_excenter_singleton_eq_add_piproof · cited by 1
- Affine.Simplex.touchpoint_empty_injectiveproof · cited by 1
- Affine.Triangle.oangle_excenter_singleton_eqproof · cited by 1