∀ {C₁ : Type u_1} {C₂ : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] {W₁ : CategoryTheory.MorphismProperty C₁}
  {W₂ : CategoryTheory.MorphismProperty C₂} {Φ : CategoryTheory.LocalizerMorphism W₁ W₂} {X₂ : C₂}
  {L L' : Φ.LeftResolution X₂} (self : L.Hom L') {Z : C₂} (h : X₂ ⟶ Z),
  CategoryTheory.CategoryStruct.comp (Φ.functor.map self.f) (CategoryTheory.CategoryStruct.comp L'.w h) =
    CategoryTheory.CategoryStruct.comp L.w h