∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {A : CategoryTheory.Functor Cᵒᵖ (Type u_2)}
  {F : CategoryTheory.Functor (CategoryTheory.CostructuredArrow CategoryTheory.yoneda A)ᵒᵖ (Type u_2)} {X Y : C}
  (f : X ⟶ Y) (p : CategoryTheory.OverPresheafAux.YonedaCollection F Y),
  Opposite.op
      (CategoryTheory.CostructuredArrow.mk (CategoryTheory.CategoryStruct.comp (CategoryTheory.yoneda.map f) p.fst)) =
    Opposite.op (CategoryTheory.CostructuredArrow.mk (CategoryTheory.OverPresheafAux.YonedaCollection.map₂ F f p).fst)