∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : HomotopicalAlgebra.ModelCategory C]
  {D : Type u_4} [inst_2 : CategoryTheory.Category.{u_3, u_4} D] (L : CategoryTheory.Functor C D)
  [L.IsLocalization (HomotopicalAlgebra.weakEquivalences C)] (x x_1 : HomotopicalAlgebra.CofibrantObject C)
  (x_2 x_3 : x ⟶ x_1),
  HomotopicalAlgebra.CofibrantObject.homRel C x_2 x_3 →
    (HomotopicalAlgebra.CofibrantObject.ι.comp L).map x_2 = (HomotopicalAlgebra.CofibrantObject.ι.comp L).map x_3