∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
  (f : X ⟶ Y)
  (h :
    (HomotopicalAlgebra.cofibrations C).MapFactorizationData (HomotopicalAlgebra.trivialFibrations C)
      (CategoryTheory.Limits.coprod.desc f (CategoryTheory.CategoryStruct.id Y))),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.coprod.inr h.i) h.p =
    CategoryTheory.CategoryStruct.id Y