∀ {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),
  (CategoryTheory.LocalizerMorphism.LeftResolution.opEquivalence Φ X₂).functor =
    CategoryTheory.LocalizerMorphism.LeftResolution.opFunctor Φ X₂