∀ {ι : Type u_1} [inst : LinearOrder ι] {X : ι → Type u_2} {i : ι} (hi : Order.IsSuccPrelimit i),
  Function.LeftInverse
    (fun f l =>
      let k := hi.mid ⋯;
      ↑f ⟨↑k, ⋯⟩ ⟨↑l, ⋯⟩)
    fun f => ⟨fun j => InverseSystem.piLTProj ⋯ f, ⋯⟩