∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C]
  (F :
    CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ)
      (CategoryTheory.Bicategory.Adj CategoryTheory.Cat))
  (ι : Type u_5) {X S : C} (f : X ⟶ S)
  (A : (CategoryTheory.Adjunction.ofCat (F.map f.op.toLoc).adj).toComonad.Coalgebra) (x x x : ι),
  CategoryTheory.CategoryStruct.comp A.a ((CategoryTheory.Adjunction.ofCat (F.map f.op.toLoc).adj).toComonad.map A.a) =
    CategoryTheory.CategoryStruct.comp A.a
      ((CategoryTheory.Adjunction.ofCat (F.map f.op.toLoc).adj).toComonad.δ.app A.A)