∀ {V : Type u_1} {G : SimpleGraph V} {w : V} [inst : DecidableEq V] {a v w_1 : V} (h : G.Adj a v) (p : G.Walk v w_1),
  (∀ (h : w ∈ p.support), (p.dropUntil w h).support = ((p.drop (List.idxOf w p.support)).copy ⋯ ⋯).support) →
    ∀ (h_1 : w ∈ (SimpleGraph.Walk.cons h p).support) (h' : w ≠ a),
      (if hx : a = w then
            Eq.rec (motive := fun x x_1 => x ∈ (SimpleGraph.Walk.cons h p).support → G.Walk x w_1)
              (fun h_2 => SimpleGraph.Walk.cons h p) hx h_1
          else p.dropUntil w ⋯).support =
        ((p.drop (List.idxOf w (SimpleGraph.Walk.cons h p).support - 1)).copy ⋯ ⋯).support