Theorems · Definition · combinatorics
SimpleGraph.Walk.transfer
{V : Type u} →
{G : SimpleGraph V} → {u v : V} → (p : G.Walk u v) → (H : SimpleGraph V) → (∀ e ∈ p.edges, e ∈ H.edgeSet) → H.Walk u vThe walk p transferred to lie in H, given that H contains its edges.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Walkstatement and proof · cited by 915
- Sym2statement and proof · cited by 737
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.Walk.edgesstatement and proof · cited by 145
- SimpleGraph.Walk.brecOnproof · cited by 15
Cited by17
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.toDeleteEdgesproof · cited by 8
- SimpleGraph.Walk.edges_transferstatement and proof · cited by 5
- SimpleGraph.reachable_deleteEdges_iff_exists_walkproof · cited by 3
- SimpleGraph.Walk.IsCycle.transferstatement and proof · cited by 3
- SimpleGraph.Walk.IsPath.transferstatement and proof · cited by 2
- SimpleGraph.Walk.transfer_eq_map_ofLEstatement and proof · cited by 1
- SimpleGraph.Walk.transfer_selfstatement and proof · cited by 1
- SimpleGraph.Walk.transfer_transferstatement and proof · cited by 1
- SimpleGraph.Walk.support_transferstatement and proof · cited by 1
- SimpleGraph.isAcyclic_sSup_of_isAcyclic_directedOnproof · cited by 1
- SimpleGraph.Walk.transfer.congr_simpstatement and proof · cited by 1
- SimpleGraph.IsBridge.sup_edge_of_not_reachable_of_isBridgeproof · cited by 1