∀ {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] {c : M}
  (f : SmoothBumpFunction I c) [inst_5 : FiniteDimensional ℝ E] {s : Set M},
  IsClosed s → s ⊆ Function.support ↑f → IsClosed (↑(extChartAt I c) '' s)