∀ {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 D)
  (c : CategoryTheory.Limits.Cone K) (j : J),
  CategoryTheory.CategoryStruct.comp (adj.counit.app c.pt)
      (((CategoryTheory.Functor.id (CategoryTheory.Limits.Cone K)).obj c).π.app j) =
    (((CategoryTheory.Limits.Cones.functoriality K G).comp (adj.functorialityLeftAdjoint K)).obj c).π.app j