Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsTrail.length_le_card_edgeFinset
∀ {V : Type u} {G : SimpleGraph V} [inst : Fintype ↑G.edgeSet] {u v : V} {w : G.Walk u v},
w.IsTrail → w.length ≤ G.edgeFinset.card- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 2 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardstatement and proof · cited by 2,327
- SimpleGraph.Walkstatement and proof · cited by 915
- Sym2statement and proof · cited by 737
- SimpleGraph.Walk.lengthstatement and proof · cited by 212
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.Walk.edgesproof · cited by 145
- Finset.card_le_cardproof · cited by 118
- SimpleGraph.edgeFinsetstatement and proof · cited by 116
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.exists_isPath_forall_isPath_length_le_lengthproof · cited by 1
- SimpleGraph.Walk.exists_isTrail_forall_isTrail_length_le_lengthproof · cited by 0