∀ {α β : Type u_1} {P : β → Prop} [inst : Std.Iterator α Id β] {it : Std.Iter β}
  {hP : ∀ (out : β), it.IsPlausibleIndirectOutput out → P out} [Std.Iterators.Finite α Id]
  [inst_2 : Std.IteratorLoop α Id Id] [Std.LawfulIteratorLoop α Id Id], (it.attachWith P hP).length = it.length