Theorems · Theorem · combinatorics
SimpleGraph.Subgraph.adj_iff_of_neighborSet_equiv
∀ {V : Type u} {G : SimpleGraph V} {v : V} {H : G.Subgraph} (h : ↑(G.neighborSet v) ≃ ↑(H.neighborSet v)),
(G.neighborSet v).Finite → ∀ {w : V}, H.Adj v w ↔ G.Adj v w- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement and proof · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Set.Finitestatement and proof · cited by 1,814
- SimpleGraph.Adjstatement · cited by 1,346
- SimpleGraph.Subgraphstatement and proof · cited by 326
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.Subgraph.Adjstatement · cited by 147
- Set.ext_iffproof · cited by 90
- SimpleGraph.Subgraph.neighborSetstatement and proof · cited by 46
- SimpleGraph.Subgraph.neighborSet_eq_of_equivproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.IsCycles.snd_of_mem_support_of_isPath_of_adjproof · cited by 0
- SimpleGraph.Walk.IsCycle.adj_toSubgraph_iff_of_isCyclesproof · cited by 0