Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsPath.length_lt
∀ {V : Type u} {G : SimpleGraph V} [inst : Fintype V] {u v : V} {p : G.Walk u v}, p.IsPath → p.length < Fintype.card V- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Fintype.cardstatement and proof · cited by 1,386
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.lengthstatement · cited by 212
- SimpleGraph.Walk.IsPathstatement and proof · cited by 140
- SimpleGraph.Walk.length_supportproof · cited by 15
- SimpleGraph.Walk.IsPath.support_nodupproof · cited by 8
- List.Nodup.length_le_cardproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.reachable_iff_exists_finsetWalkLength_nonemptyproof · cited by 0