Theorems · Theorem · combinatorics
SimpleGraph.Walk.length_takeUntil_lt_length
∀ {V : Type u} {G : SimpleGraph V} [inst : DecidableEq V] {u v w : V} {p : G.Walk v w} (h : u ∈ p.support),
u ≠ w → (p.takeUntil u h).length < p.length- Cited by
- 4 results in Mathlib
- Foundations
- Depth 74 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.
Cites10
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
- le_reflproof · cited by 2,061
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.supportstatement and proof · cited by 307
- SimpleGraph.Walk.lengthstatement and proof · cited by 212
- SimpleGraph.Walk.takeUntilstatement and proof · cited by 58
- LE.le.lt_iff_neproof · cited by 34
- SimpleGraph.Walk.getVert_lengthproof · cited by 11
- SimpleGraph.Walk.getVert_takeUntilproof · cited by 4
- SimpleGraph.Walk.length_takeUntil_le_lengthproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.IsPath.exists_isCycle_of_neproof · cited by 2
- SimpleGraph.Walk.endpoint_notMem_support_takeUntilproof · cited by 1
- SimpleGraph.Walk.notMem_support_takeUntil_support_takeUntil_subsetproof · cited by 1
- SimpleGraph.Walk.length_takeUntil_ltproof · cited by 0