(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : C} →
      {f : X ⟶ X} →
        CategoryTheory.CategoryStruct.comp f f = f →
          [inst_1 : CategoryTheory.Limits.HasCoequalizer (CategoryTheory.CategoryStruct.id X) f] →
            CategoryTheory.SplitEpi (CategoryTheory.Limits.coequalizer.π (CategoryTheory.CategoryStruct.id X) f)