{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : HomotopicalAlgebra.ModelCategory C] →
      {X Y : C} →
        {f : X ⟶ Y} →
          {motive : HomotopicalAlgebra.FibrantBrownFactorization f → Sort u} →
            ((toMapFactorizationData :
                  (HomotopicalAlgebra.trivialCofibrations C).MapFactorizationData (HomotopicalAlgebra.fibrations C) f) →
                (r : toMapFactorizationData.Z ⟶ X) →
                  (i_r :
                      CategoryTheory.CategoryStruct.comp toMapFactorizationData.i r =
                        CategoryTheory.CategoryStruct.id X) →
                    (fibration_r : HomotopicalAlgebra.Fibration r) →
                      motive
                        { toMapFactorizationData := toMapFactorizationData, r := r, i_r := i_r,
                          fibration_r := fibration_r }) →
              (t : HomotopicalAlgebra.FibrantBrownFactorization f) → motive t