{EB : Type u_1} →
  [inst : NormedAddCommGroup EB] →
    [inst_1 : NormedSpace ℝ EB] →
      {HB : Type u_2} →
        [inst_2 : TopologicalSpace HB] →
          {IB : ModelWithCorners ℝ EB HB} →
            {n : WithTop ℕ∞} →
              {B : Type u_3} →
                [inst_3 : TopologicalSpace B] →
                  [inst_4 : ChartedSpace HB B] →
                    {F : Type u_4} →
                      [inst_5 : NormedAddCommGroup F] →
                        [inst_6 : NormedSpace ℝ F] →
                          {E : B → Type u_5} →
                            [inst_7 : TopologicalSpace (Bundle.TotalSpace F E)] →
                              [inst_8 : (x : B) → NormedAddCommGroup (E x)] →
                                [inst_9 : (x : B) → InnerProductSpace ℝ (E x)] →
                                  [inst_10 : FiberBundle F E] →
                                    [inst_11 : VectorBundle ℝ F E] →
                                      {motive : IsContMDiffRiemannianBundle IB n F E → Sort u} →
                                        ((exists_contMDiff :
                                              ∃ g,
                                                (ContMDiff IB (IB.prod (modelWithCornersSelf ℝ (F →L[ℝ] F →L[ℝ] ℝ))) n
                                                    fun b => ⟨b, g b⟩) ∧
                                                  ∀ (x : B) (v w : E x), inner ℝ v w = ((g x) v) w) →
                                            motive ⋯) →
                                          (t : IsContMDiffRiemannianBundle IB n F E) → motive t