Theorems · Theorem · convex and discrete geometry
convexHull_nonempty_iff
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] {s : Set E}, ((convexHull 𝕜) s).Nonempty ↔ s.Nonempty- Defined in
- Mathlib.Analysis.Convex.Hull
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Set.Nonemptystatement and proof · cited by 2,627
- ClosureOperatorstatement · cited by 371
- convexHullstatement and proof · cited by 163
- Set.nonempty_iff_ne_emptyproof · cited by 96
- convexHull_eq_emptyproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Set.Nonempty.convexHullproof · cited by 1
- Caratheodory.minCardFinsetOfMemConvexHull_nonemptyproof · cited by 1
- ConvexOn.le_sup_of_mem_convexHullstatement · cited by 1
- Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHullproof · cited by 0
- ConvexOn.inf_le_of_mem_convexHullstatement · cited by 0
- Subsingleton.convexIndependentproof · cited by 0