Theorems · Theorem · algebraic topology
SSet.Subcomplex.Pairing.RankFunction.lt
∀ {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {α : Type v} [inst : PartialOrder α] (self : P.RankFunction α)
{x y : ↑P.II}, P.AncestralRel x y → self.rank x < self.rank y- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
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.
- Set.Elemstatement · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- SSet.Subcomplex.Nstatement · cited by 155
- SSet.Subcomplex.Pairingstatement and proof · cited by 117
- SSet.Subcomplex.Pairing.RankFunctionstatement and proof · cited by 68
- SSet.Subcomplex.Pairing.IIstatement · cited by 58
- SSet.Subcomplex.Pairing.AncestralRelstatement · cited by 22
- SSet.Subcomplex.Pairing.RankFunction.rankstatement · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.Pairing.RankFunction.toWeakRankFunctionproof · cited by 1
- SSet.Subcomplex.Pairing.RankFunction.wf_ancestralRelproof · cited by 1
- SSet.Subcomplex.Pairing.RankFunction.Cell.preimage_filtration_mapproof · cited by 1
- SSet.Subcomplex.Pairing.RankFunction.Cell.subcomplex_not_le_filtrationproof · cited by 1