Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.Subgraph.coeNeighborSetEquiv

{V : Type u} →
  {G : SimpleGraph V} → {G' : G.Subgraph} → (v : ↑G'.verts) → ↑(G'.coe.neighborSet v) ≃ ↑(G'.neighborSet ↑v)

A subgraph as a graph has equivalent neighbor sets.

Defined in
Mathlib.Combinatorics.SimpleGraph.Subgraph
Cited by
1 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.Subgraph.coe_degree · cited by 3Subgraph.coe_degreeSet · cited by 53352SetEquiv · cited by 8337EquivSet.Elem · cited by 7166Set.ElemSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Subgraph · cited by 326SimpleGraph.SubgraphSimpleGraph.neighborSet · cited by 257SimpleGraph.neighborSetSimpleGraph.Subgraph.verts · cited by 210Subgraph.vertsSimpleGraph.Subgraph.coe · cited by 89Subgraph.coeSimpleGraph.Subgraph.neighborSet · cited by 46Subgraph.neighborSetSubgraph.coeNeighborSetEquivCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.