{B : Type u_1} →
  [inst : TopologicalSpace B] →
    {F₁ : Type u_2} →
      [inst_1 : TopologicalSpace F₁] →
        {E₁ : B → Type u_3} →
          [inst_2 : TopologicalSpace (Bundle.TotalSpace F₁ E₁)] →
            {F₂ : Type u_4} →
              [inst_3 : TopologicalSpace F₂] →
                {E₂ : B → Type u_5} →
                  [inst_4 : TopologicalSpace (Bundle.TotalSpace F₂ E₂)] →
                    Trivialization F₁ Bundle.TotalSpace.proj →
                      Trivialization F₂ Bundle.TotalSpace.proj →
                        (Bundle.TotalSpace (F₁ × F₂) fun x => E₁ x × E₂ x) → B × F₁ × F₂