∀ {C : Type u_6} [inst : CategoryTheory.Category.{u_5, u_6} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{u_1, u_2} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G) {J : Type u_4} [inst_2 : CategoryTheory.Category.{u_3, u_4} J] (K : CategoryTheory.Functor J C)
  (c : CategoryTheory.Limits.Cocone (K.comp F)) (j : J),
  CategoryTheory.CategoryStruct.comp
      ((((adj.functorialityRightAdjoint K).comp (CategoryTheory.Limits.Cocones.functoriality K F)).obj c).ι.app j)
      (adj.counit.app c.pt) =
    ((CategoryTheory.Functor.id (CategoryTheory.Limits.Cocone (K.comp F))).obj c).ι.app j