∀ {V : Type u_1} {G : SimpleGraph V} (G' : G.Subgraph) (x x_1 : V),
  (∃ a, ∃ (h : a ∈ G'.verts), ∃ a_1, ∃ (h_1 : a_1 ∈ G'.verts), G'.coe.Adj ⟨a, ⋯⟩ ⟨a_1, ⋯⟩ ∧ a = x ∧ a_1 = x_1) ↔
    G'.spanningCoe.Adj x x_1