Sort u →
  {ι : Type uι} →
    {E : Type uE} →
      [inst : NormedAddCommGroup E] →
        [inst_1 : NormedSpace ℝ E] →
          {H : Type uH} →
            [inst_2 : TopologicalSpace H] →
              {I : ModelWithCorners ℝ E H} →
                {M : Type uM} →
                  [inst_3 : TopologicalSpace M] →
                    [inst_4 : ChartedSpace H M] →
                      {s : Set M} →
                        SmoothPartitionOfUnity ι I M s →
                          {ι' : Type uι} →
                            {E' : Type uE} →
                              [inst' : NormedAddCommGroup E'] →
                                [inst'_1 : NormedSpace ℝ E'] →
                                  {H' : Type uH} →
                                    [inst'_2 : TopologicalSpace H'] →
                                      {I' : ModelWithCorners ℝ E' H'} →
                                        {M' : Type uM} →
                                          [inst'_3 : TopologicalSpace M'] →
                                            [inst'_4 : ChartedSpace H' M'] →
                                              {s' : Set M'} → SmoothPartitionOfUnity ι' I' M' s' → Sort u