{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {A : C} →
      [inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C] →
        HomotopicalAlgebra.Cylinder A →
          [CategoryTheory.Limits.HasBinaryCoproduct A A] →
            [HomotopicalAlgebra.CategoryWithCofibrations C] → [HomotopicalAlgebra.CategoryWithFibrations C] → Prop