∀ {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 (HomotopicalAlgebra.CofibrantObject.HoCat C) D)
  [L.IsLocalization (HomotopicalAlgebra.weakEquivalences (HomotopicalAlgebra.CofibrantObject.HoCat C))],
  (HomotopicalAlgebra.CofibrantObject.toHoCat.comp L).IsLocalization
    (HomotopicalAlgebra.weakEquivalences (HomotopicalAlgebra.CofibrantObject C))