Theorems · Theorem · combinatorics
SimpleGraph.Walk.IsCycle.transfer
∀ {V : Type u} {G : SimpleGraph V} {u : V} {H : SimpleGraph V} {q : G.Walk u u},
q.IsCycle → ∀ (hq : ∀ e ∈ q.edges, e ∈ H.edgeSet), (q.transfer H hq).IsCycle- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjproof · cited by 1,346
- SimpleGraph.Walkstatement and proof · cited by 915
- Sym2statement and proof · cited by 737
- Sym2.mkproof · cited by 332
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.Walk.edgesstatement and proof · cited by 145
- SimpleGraph.Walk.IsPathproof · cited by 140
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.Walk.casesOnproof · cited by 59
- SimpleGraph.Walk.transferstatement and proof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.isAcyclic_sSup_of_isAcyclic_directedOnproof · cited by 1
- SimpleGraph.IsBridge.sup_edge_of_not_reachable_of_isBridgeproof · cited by 1
- SimpleGraph.Walk.IsCycle.toDeleteEdgesproof · cited by 0