∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y W : C} (f : X ⟶ Y)
  [inst_1 : CategoryTheory.IsRegularMono f] (k : W ⟶ Y)
  (h :
    CategoryTheory.CategoryStruct.comp k (CategoryTheory.IsRegularMono.left f) =
      CategoryTheory.CategoryStruct.comp k (CategoryTheory.IsRegularMono.right f))
  (m : W ⟶ X), CategoryTheory.CategoryStruct.comp m f = k → m = CategoryTheory.IsRegularMono.lift f k h