Theorems · Theorem · convex and discrete geometry
Geometry.SimplicialComplex.nonempty_of_mem_faces
∀ {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}, s ∈ K.faces → s.Nonempty- Cited by
- 1 results in Mathlib
- Foundations
- Depth 56 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.
- Setstatement · 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
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Finset.Nonemptystatement · cited by 1,001
- PreAbstractSimplicialComplex.facesstatement and proof · cited by 36
- Geometry.SimplicialComplexstatement and proof · cited by 27
- Geometry.SimplicialComplex.toPreAbstractSimplicialComplexstatement and proof · cited by 23
- PreAbstractSimplicialComplex.isRelLowerSet_facesproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Geometry.SimplicialComplex.empty_notMemproof · cited by 0