∀ {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} {f : BumpCovering ι M s} {U : ι → Set M},
  f.IsSubordinate U →
    ∀ (hf : ∀ (i : ι), ContMDiff I (modelWithCornersSelf ℝ ℝ) ↑⊤ ⇑(f i)),
      (f.toSmoothPartitionOfUnity hf).IsSubordinate U