∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {W : CategoryTheory.MorphismProperty C} {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (L : CategoryTheory.Functor C D) [inst_2 : L.IsLocalization W] {X Y : C}
  [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y]
  [inst_4 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y] (e : CategoryTheory.Localization.SmallHom W X Y),
  (CategoryTheory.Localization.SmallHom.equiv W L) (CategoryTheory.Localization.SmallHom.chgUniv e) =
    (CategoryTheory.Localization.SmallHom.equiv W L) e