Theorems · Theorem · convex and discrete geometry
convexIndependent_set_iff_inter_convexHull_subset
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] {s : Set E}, ConvexIndependent 𝕜 Subtype.val ↔ ∀ t ⊆ s, s ∩ (convexHull 𝕜) t ⊆ t- Defined in
- Mathlib.Analysis.Convex.Independent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Subtype.propproof · cited by 505
- ClosureOperatorstatement · cited by 371
- Subtype.coe_injectiveproof · cited by 205
- convexHullstatement and proof · cited by 163
Cited by1
Results whose statement or proof uses this declaration.
- convexIndependent_set_iff_notMem_convexHull_sdiffproof · cited by 2