Theorems · Theorem · convex and discrete geometry
Convex.convexHull_eq
∀ {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}, Convex 𝕜 s → (convexHull 𝕜) s = sAlias of the reverse direction of convexHull_eq_self.
- Defined in
- Mathlib.Analysis.Convex.Hull
- Cited by
- 8 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Convexstatement · cited by 551
- ClosureOperatorstatement · cited by 371
- convexHullstatement · cited by 163
- convexHull_eq_selfproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- convexHull_singletonproof · cited by 7
- convexHull_emptyproof · cited by 3
- Convex.interior_nonempty_iff_affineSpan_eq_topproof · cited by 2
- TotallyBounded.convexHullproof · cited by 1
- Convex.convex_remove_iff_notMem_convexHull_removeproof · cited by 1
- exists_convex_convex_compl_subsetproof · cited by 0
- Convex.exists_subset_interior_convexHull_finset_of_isCompactproof · cited by 0
- convexHull_union_neg_eq_absConvexHullproof · cited by 0