Theorems · Definition · algebraic topology
SSet.Path.interval
{X : SSet} → {n : ℕ} → X.Path n → (j l : ℕ) → autoParam (j + l ≤ n) SSet.Path.interval._auto_1 → X.Path lFor j + l ≤ n, a path of length n restricts to a path of length l, namely
the subpath spanned by the vertices j ≤ i ≤ j + l and edges j ≤ i < j + l.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SSetstatement and proof · cited by 1,283
- SSet.Pathstatement and proof · cited by 46
- SSet.Truncated.Path.intervalproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- SSet.StrictSegalCore.spineToSimplex_succstatement · cited by 2
- SSet.StrictSegal.spineToSimplex_edgestatement · cited by 1
- SSet.StrictSegal.spineToSimplex_intervalstatement and proof · cited by 1
- SSet.StrictSegal.spine_δ_arrow_eqstatement and proof · cited by 1
- SSet.StrictSegalCore.map_mkOfSucc_zero_spineToSimplexproof · cited by 1
- SSet.StrictSegalCore.spineToSimplexAuxproof · cited by 1
- SSet.Path.arrow_intervalstatement · cited by 1
- SSet.spine_map_subintervalstatement · cited by 1
- SSet.StrictSegalCore.δ₀_spineToSimplexstatement and proof · cited by 1
- SSet.spine_δ₀statement and proof · cited by 1
- SSet.StrictSegalCore.spineToSimplex_spineproof · cited by 0
- SSet.Path.interval.congr_simpstatement and proof · cited by 0