Theorems · Theorem · convex and discrete geometry
Geometry.SimplicialComplex.not_facet_iff_subface
∀ {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 ∉ K.facets ↔ ∃ t ∈ K.faces, s ⊂ t)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- PreAbstractSimplicialComplex.facesstatement and proof · cited by 36
- Finset.Subset.reflproof · cited by 29
- Geometry.SimplicialComplexstatement and proof · cited by 27
- Geometry.SimplicialComplex.toPreAbstractSimplicialComplexstatement and proof · cited by 23
- Finset.Subset.antisymmproof · cited by 12
- Geometry.SimplicialComplex.facetsstatement and proof · cited by 4
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