Theorems · Theorem · convex and discrete geometry
convexHull_eq_union_convexHull_finite_subsets
∀ {R : Type u_1} {E : Type u_3} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
[inst_3 : LinearOrder R] [IsStrictOrderedRing R] (s : Set E),
(convexHull R) s = ⋃ t, ⋃ (_ : ↑t ⊆ s), (convexHull R) ↑tA weak version of Carathéodory's theorem.
- Defined in
- Mathlib.Analysis.Convex.Combination
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement and proof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- Finset.sumproof · cited by 5,195
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Set.iUnionstatement and proof · cited by 2,483
Cited by1
Results whose statement or proof uses this declaration.
- convexIndependent_iff_finsetproof · cited by 0