Theorems · Theorem · algebraic topology
SSet.dim_lt_of_nonDegenerate
∀ (X : SSet) {n : ℕ} (x : ↑(X.nonDegenerate n)) (d : ℕ) [X.HasDimensionLT d], n < d- Cited by
- 7 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SSet.HasDimensionLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- Set.Elemstatement and proof · cited by 7,166
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.nonDegeneratestatement and proof · cited by 106
- SSet.HasDimensionLTstatement and proof · cited by 32
- SSet.nonDegenerate_eq_empty_of_hasDimensionLTproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.not_hasDimensionLTproof · cited by 1
- SSet.Subcomplex.le_iff_of_hasDimensionLTproof · cited by 1
- SSet.hasDimensionLT_prodproof · cited by 1
- SSet.relativeCellComplexOfMono.Cell.preimage_mapproof · cited by 1
- SSet.isZero_normalizedChainComplex_X_of_hasDimensionLTproof · cited by 1
- SSet.notNonempty_iff_hasDimensionLT_zeroproof · cited by 0
- SSet.dim_le_of_nonDegenerateproof · cited by 0