∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P₁ P₂ : CategoryTheory.Functor Cᵒᵖ (Type (max w v₁))}
  (α : P₁ ⟶ P₂) (j : P₁.Elementsᵒᵖ),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Presheaf.coconeOfRepresentable P₁).ι.app j) α =
    (CategoryTheory.Presheaf.coconeOfRepresentable P₂).ι.app ((CategoryTheory.CategoryOfElements.map α).op.obj j)