Theorems · Theorem · convex and discrete geometry
Affine.Simplex.dist_lt_of_mem_closedInterior_of_strictConvexSpace
∀ {V : Type u_2} {P : Type u_3} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [StrictConvexSpace ℝ V]
[inst_3 : PseudoMetricSpace P] [inst_4 : NormedAddTorsor V P] {n : ℕ} (s : Affine.Simplex ℝ P n) {r : ℝ} {p₀ p : P},
p ∈ s.closedInterior →
(∀ (i : Fin (n + 1)), p ≠ s.points i) → (∀ (i : Fin (n + 1)), dist (s.points i) p₀ ≤ r) → dist p p₀ < r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- Set.Iccproof · cited by 1,702
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.dist_lt_of_mem_interior_of_strictConvexSpaceproof · cited by 1