Theorems · Theorem · convex and discrete geometry
Finset.mem_convexHull
∀ {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 : Finset E} {x : E},
x ∈ (convexHull R) ↑s ↔ ∃ w, (∀ y ∈ s, 0 ≤ w y) ∧ ∑ y ∈ s, w y = 1 ∧ s.centerMass w id = x- Defined in
- Mathlib.Analysis.Convex.Combination
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Finset.sumstatement and proof · cited by 5,195
- IsStrictOrderedRingstatement and proof · cited by 2,490
- ClosureOperatorstatement · cited by 371
- convexHullstatement · cited by 163
Cited by2
Results whose statement or proof uses this declaration.
- ConvexOn.le_sup_of_mem_convexHullproof · cited by 1
- Finset.mem_convexHull'proof · cited by 0