∀ {α β : Type w} [inst : Std.Iterator α Id β] {a : Std.Iter β}
  {motive : (a_1 : Std.Iter β) → a.IsPlausibleIndirectSuccessorOf a_1 → Prop} {a_1 : Std.Iter β}
  (t : a.IsPlausibleIndirectSuccessorOf a_1),
  motive a ⋯ →
    (∀ {it' it : Std.Iter β} (h' : a.IsPlausibleIndirectSuccessorOf it') (h : it'.IsPlausibleSuccessorOf it),
        motive it' h' → motive it ⋯) →
      motive a_1 t