∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f g : X ⟶ Y}
  [inst_1 : CategoryTheory.Limits.HasEqualizer f g] {W : C} (k : W ⟶ X)
  (h : CategoryTheory.CategoryStruct.comp k f = CategoryTheory.CategoryStruct.comp k g),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.equalizer.lift k h)
      (CategoryTheory.Limits.equalizer.ι f g) =
    k