∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (r : HomRel C) {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F G H : CategoryTheory.Functor (CategoryTheory.Quotient r) D}
  (τ : (CategoryTheory.Quotient.functor r).comp F ⟶ (CategoryTheory.Quotient.functor r).comp G)
  (τ' : (CategoryTheory.Quotient.functor r).comp G ⟶ (CategoryTheory.Quotient.functor r).comp H),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Quotient.natTransLift r τ)
      (CategoryTheory.Quotient.natTransLift r τ') =
    CategoryTheory.Quotient.natTransLift r (CategoryTheory.CategoryStruct.comp τ τ')