∀ {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 s) ((SimpleGraph.induce s G).neighborFinset v) = G.neighborFinset ↑v