∀ {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] [inst_5 : FiniteDimensional ℝ E] {s : Set M} [inst_6 : T2Space M]
  [inst_7 : IsManifold I (↑⊤) M] {f : SmoothBumpCovering ι I M s} {U : M → Set M},
  (f.toBumpCovering.IsSubordinate fun i => U (f.c i)) = f.IsSubordinate U