Theorems · Theorem · convex and discrete geometry
convexHull_mono
∀ {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 → (convexHull 𝕜) s ⊆ (convexHull 𝕜) t- Defined in
- Mathlib.Analysis.Convex.Hull
- Cited by
- 13 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.
Cites9
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
- ClosureOperatorstatement · cited by 371
- convexHullstatement and proof · cited by 163
- ClosureOperator.monotoneproof · cited by 18
Cited by13
Results whose statement or proof uses this declaration.
- absConvexHull_eq_convexHull_balancedHullproof · cited by 2
- convexIndependent_set_iff_notMem_convexHull_sdiffproof · cited by 2
- AffineIndependent.convexHull_interproof · cited by 1
- TotallyBounded.convexHullproof · cited by 1
- Geometry.SimplicialComplex.convexHull_inter_convexHullproof · cited by 1
- convexHull_eq_unionproof · cited by 1
- convexHull_eq_union_convexHull_finite_subsetsproof · cited by 1
- interior_convexHull_nonempty_iff_affineSpan_eq_topproof · cited by 1
- sphere_subset_range_iff_surjectiveproof · cited by 0
- Convex.exists_subset_interior_convexHull_finset_of_isCompactproof · cited by 0
- convexHull_union_neg_eq_absConvexHullproof · cited by 0
- AmpleSet.unionproof · cited by 0