Theorems · Theorem · algebraic topology
SSet.subcomplex_le_horn_iff
∀ {n : ℕ} (A : (SSet.stdSimplex.obj { len := n + 1 }).Subcomplex) (i : Fin (n + 2)),
A ≤ SSet.horn (n + 1) i ↔ ¬SSet.stdSimplex.face {i}ᶜ ≤ A- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites49
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Finsetstatement and proof · cited by 13,712
- Oppositestatement · cited by 8,081
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- Equiv.symmproof · cited by 3,681
- Finset.univproof · cited by 3,473
- LE.le.transproof · cited by 3,151
Cited by2
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.Pairing.RankFunction.Cell.subcomplex_not_le_image_hornproof · cited by 2
- SSet.face_le_horn_iffproof · cited by 1