∀ {C D E : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Category.{v, u} D]
  [inst_2 : CategoryTheory.Category.{v, u} E] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G) {F' : CategoryTheory.Functor D E} {G' : CategoryTheory.Functor E D} (adj' : F' ⊣ G'),
  adj.toCat.comp adj'.toCat = (adj.comp adj').toCat