∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {A : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_3, u_4} A] (P : CategoryTheory.Functor Cᵒᵖ A) {X : C}
  (S : CategoryTheory.Sieve X) (E : Aᵒᵖ),
  Function.RightInverse (fun x => { app := fun f => ↑x (Opposite.unop f).obj.hom ⋯, naturality := ⋯ }) fun π =>
    ⟨fun x f h => π.app (Opposite.op { obj := CategoryTheory.Over.mk f, property := h }), ⋯⟩