∀ {V : Type u_1} {G : SimpleGraph V} (G' : G.Subgraph) (h : G'.IsSpanning) {a b : V},
  G'.coe.Adj ({ toFun := fun v => ⟨v, ⋯⟩, invFun := fun v => ↑v, left_inv := ⋯, right_inv := ⋯ } a)
      ({ toFun := fun v => ⟨v, ⋯⟩, invFun := fun v => ↑v, left_inv := ⋯, right_inv := ⋯ } b) ↔
    G'.coe.Adj ({ toFun := fun v => ⟨v, ⋯⟩, invFun := fun v => ↑v, left_inv := ⋯, right_inv := ⋯ } a)
      ({ toFun := fun v => ⟨v, ⋯⟩, invFun := fun v => ↑v, left_inv := ⋯, right_inv := ⋯ } b)