Affine.Simplex.incenter_mem_affineSpan_range
∀ {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),
s.incenter ∈ affineSpan ℝ (Set.range s.points)- Defined in
- Mathlib.Geometry.Euclidean.Incenter
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Set.rangestatement · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement · cited by 871
- Affine.Simplexstatement and proof · cited by 471
- affineSpanstatement · cited by 417
- Affine.Simplex.pointsstatement · cited by 391
- Affine.Simplex.incenterstatement · cited by 35
- Affine.Simplex.excenterExists_emptyproof · cited by 28
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