Theorems · Theorem · combinatorics

SimpleGraph.map_neighborFinset_induce_of_neighborSet_subset

∀ {V : Type u_1} {s : Set V} [inst : DecidablePred fun x => x ∈ s] [inst_1 : Fintype V] {G : SimpleGraph V}
  [inst_2 : DecidableRel G.Adj] {v : ↑s},
  G.neighborSet ↑v ⊆ s →
    Finset.map (Function.Embedding.subtype fun x => x ∈ s) ((SimpleGraph.induce s G).neighborFinset v) =
      G.neighborFinset ↑v

Defined in

Mathlib.Combinatorics.SimpleGraph.Finite

Cited by

1 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidablePredFintypeDecidableRel