Theorems · Theorem · convex and discrete geometry
convexHull_smul
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : CommSemiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] (a : 𝕜) (s : Set E), (convexHull 𝕜) (a • s) = a • (convexHull 𝕜) s- Defined in
- Mathlib.Analysis.Convex.Hull
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- PartialOrderstatement and proof · cited by 6,410
- Set.smulSetstatement · cited by 608
- ClosureOperatorstatement · cited by 371
- convexHullstatement · cited by 163
- LinearMap.lsmulproof · cited by 50
- LinearMap.image_convexHullproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- exists_mem_interior_convexHull_affineBasisproof · cited by 2