Theorems · Theorem · combinatorics
SimpleGraph.Walk.endpoint_notMem_support_takeUntil
∀ {V : Type u} {G : SimpleGraph V} {u v w : V} [inst : DecidableEq V] {p : G.Walk u v},
p.IsPath → ∀ (hw : w ∈ p.support), v ≠ w → v ∉ (p.takeUntil w hw).supportTaking a strict initial segment of a path removes the end vertex from the support.
- 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
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.supportstatement and proof · cited by 307
- SimpleGraph.Walk.lengthproof · cited by 212
- SimpleGraph.Walk.IsPathstatement and proof · cited by 140
- SimpleGraph.Walk.getVertproof · cited by 114
- Set.mem_ofPredproof · cited by 104
- SimpleGraph.Walk.takeUntilstatement and proof · cited by 58
- SimpleGraph.Walk.getVert_lengthproof · cited by 11
- SimpleGraph.Walk.IsPath.getVert_injOnproof · cited by 7
- SimpleGraph.Walk.getVert_takeUntilproof · cited by 4
- SimpleGraph.Walk.mem_support_iff_exists_getVertproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.Connected.connected_delete_edge_of_not_isBridgeproof · cited by 2