Theorems · Theorem · convex and discrete geometry
Geometry.SimplicialComplex.vertex_mem_convexHull_iff
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] {K : Geometry.SimplicialComplex 𝕜 E} {s : Finset E} {x : E},
x ∈ K.vertices → s ∈ K.faces → (x ∈ (convexHull 𝕜) ↑s ↔ x ∈ s)- 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.
Cites24
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
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- ClosureOperatorstatement · cited by 371
- convexHullstatement and proof · cited by 163
- Finset.coe_singletonproof · cited by 145
- Disjoint.symmproof · cited by 125
Cited by1
Results whose statement or proof uses this declaration.
- Geometry.SimplicialComplex.face_subset_face_iffproof · cited by 0