∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {P Q R S : C} {f : P ⟶ Q} {g : P ⟶ R} {h : Q ⟶ S}
  {k : R ⟶ S} (hr : CategoryTheory.RegularMono h),
  CategoryTheory.CategoryStruct.comp f h = CategoryTheory.CategoryStruct.comp g k →
    CategoryTheory.CategoryStruct.comp g (CategoryTheory.CategoryStruct.comp k hr.left) =
      CategoryTheory.CategoryStruct.comp g (CategoryTheory.CategoryStruct.comp k hr.right)