Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite
∀ {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]
(i : Fin (n + 1)), s.touchpoint ∅ i ∈ (s.faceOpposite i).interior- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement · 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
- Nat.AtLeastTwostatement and proof · cited by 405
- Affine.Simplex.faceOppositestatement · cited by 103
- Affine.Simplex.touchpointstatement and proof · cited by 49
- Affine.Simplex.faceproof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Triangle.sbtw_touchpoint_emptyproof · cited by 1