∀ {α β : Type w} {m : Type w → Type w'} [inst : Std.Iterator α m β]
  {motive :
    (a : ℕ) →
      (a_1 : Std.IterM m β) →
        (a_2 : Std.IterStep (Std.IterM m β) β) → Std.IterM.IsPlausibleNthOutputStep a a_1 a_2 → Prop}
  {n : ℕ} {it it' : Std.IterM m β} {out : β} {step : Std.IterStep (Std.IterM m β) β}
  (a : it.IsPlausibleStep (Std.IterStep.yield it' out)) (a_1 : Std.IterM.IsPlausibleNthOutputStep n it' step),
  Std.IterM.IsPlausibleNthOutputStep.below a_1 → motive n it' step a_1 → Std.IterM.IsPlausibleNthOutputStep.below ⋯