∀ {ι : Type u_1} [inst : LinearOrder ι] [inst_1 : LocallyFiniteOrder ι] [inst_2 : DecidableLE ι] {X : ι → Type u_2}
  [inst_3 : LocallyFiniteOrderBot ι] {a b : ι} (hab : a ≤ b) (x : (i : ↥(Finset.Iic b)) → X ↑i),
  (fun i =>
      if h : ↑i ≤ a then (fun i => x ⟨↑i, ⋯⟩, fun i => x ⟨↑i, ⋯⟩).1 ⟨↑i, ⋯⟩
      else (fun i => x ⟨↑i, ⋯⟩, fun i => x ⟨↑i, ⋯⟩).2 ⟨↑i, ⋯⟩) =
    x