Theorems · Theorem · convex and discrete geometry
convexHull_min
∀ {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 t : Set E}, s ⊆ t → Convex 𝕜 t → (convexHull 𝕜) s ⊆ t- Defined in
- Mathlib.Analysis.Convex.Hull
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 61 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
- ClosureOperator.closure_minproof · cited by 12
Cited by28
Results whose statement or proof uses this declaration.
- Finset.convexHull_eqproof · cited by 4
- convexHull_eqproof · cited by 3
- convexHull_pairproof · cited by 3
- AffineMap.image_convexHullproof · cited by 3
- convexHull_basis_eq_stdSimplexproof · cited by 2
- IsLinearMap.image_convexHullproof · cited by 2
- doublyStochastic_eq_convexHull_permMatrixproof · cited by 2
- absConvexHull_eq_convexHull_balancedHullproof · cited by 2
- extremePoints_convexHull_subsetproof · cited by 2
- Balanced.convexHullproof · cited by 2
- nhds_hasBasis_absConvexproof · cited by 2
- convexHull_prodproof · cited by 2