Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsPath.getVert_injOn
∀ {V : Type u} {G : SimpleGraph V} {u v : V} {p : G.Walk u v}, p.IsPath → Set.InjOn p.getVert {i | i ≤ p.length}- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Set.ofPredstatement and proof · cited by 6,101
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjproof · cited by 1,346
- SimpleGraph.Walkstatement and proof · cited by 915
- Set.InjOnstatement · cited by 543
- SimpleGraph.Walk.supportproof · cited by 307
- SimpleGraph.Walk.lengthstatement and proof · cited by 212
- SimpleGraph.Walk.IsPathstatement and proof · cited by 140
- SimpleGraph.Walk.getVertstatement and proof · cited by 114
- SimpleGraph.Walk.getVert_zeroproof · cited by 43
- SimpleGraph.Walk.getVert_consproof · cited by 5
- SimpleGraph.Walk.mem_support_iff_exists_getVertproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.IsCycle.getVert_injOnproof · cited by 4
- SimpleGraph.Walk.IsPath.getVert_eq_start_iff_of_not_nilproof · cited by 2
- SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adjproof · cited by 1
- SimpleGraph.Walk.endpoint_notMem_support_takeUntilproof · cited by 1
- SimpleGraph.Walk.IsPath.neighborSet_toSubgraph_internalproof · cited by 1
- SimpleGraph.Walk.IsPath.getVert_injOn_iffproof · cited by 0
- SimpleGraph.Walk.IsPath.ncard_neighborSet_toSubgraph_internal_eq_twoproof · cited by 0