Theorems · Theorem · algebraic topology
SSet.nonDegenerate_eq_empty_of_hasDimensionLT
∀ (X : SSet) (d : ℕ) [X.HasDimensionLT d] (n : ℕ), autoParam (d ≤ n) SSet.nonDegenerate_eq_empty_of_hasDimensionLT._auto_1 → X.nonDegenerate n = ∅
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 59 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- Compl.complproof · cited by 2,925
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.nonDegeneratestatement · cited by 106
- Set.compl_univproof · cited by 41
- SSet.HasDimensionLTstatement and proof · cited by 32
- SSet.degenerate_eq_univ_of_hasDimensionLTproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- SSet.dim_lt_of_nonDegenerateproof · cited by 7
- SSet.finite_of_hasDimensionLTproof · cited by 2
- SSet.stdSimplex.le_boundary_iffproof · cited by 2
- SSet.nonDegenerate_eq_bot_of_hasDimensionLTproof · cited by 0