∀ {V : Type u_1} {G : SimpleGraph V} {w : V} [inst : DecidableEq V] {a v_1 w_1 : V} (h_1 : G.Adj a v_1)
  (p : G.Walk v_1 w_1),
  w ≠ a →
    p.getVert (List.idxOf w (SimpleGraph.Walk.cons h_1 p).support - 1) =
      (SimpleGraph.Walk.cons h_1 p).getVert (List.idxOf w (SimpleGraph.Walk.cons h_1 p).support)