∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {E' : Type u_3} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {H : Type u_5}
  [inst_5 : TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) {M : Type u_9} [inst_6 : TopologicalSpace M]
  [inst_7 : ChartedSpace H M] (e : E ≃L[𝕜] E') (x : M),
  ↑(extChartAt (I.transContinuousLinearEquiv e) x) = ⇑e ∘ ↑(extChartAt I x)