Theorems · Theorem · algebraic topology
SSet.notNonempty_iff_hasDimensionLT_zero
∀ (X : SSet), ¬X.Nonempty ↔ X.HasDimensionLT 0
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- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objproof · cited by 19,642
- Top.topproof · cited by 9,680
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Quiver.Hom.opproof · cited by 1,948
- SSetstatement and proof · cited by 1,283
- IsEmptyproof · cited by 759
- SimplexCategory.constproof · cited by 47
- lt_self_iff_falseproof · cited by 41
- SSet.HasDimensionLTstatement and proof · cited by 32
- SSet.degenerateproof · cited by 29
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