∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s : Set M} {x : M} {V : (x : M) → TangentSpace I x}
  [inst_6 : IsManifold I 2 M] [CompleteSpace E],
  MDifferentiableWithinAt I I.tangent (fun x => { proj := x, snd := V x }) s x →
    DifferentiableWithinAt 𝕜
      (VectorField.mpullbackWithin (modelWithCornersSelf 𝕜 E) I (↑(extChartAt I x).symm) V (Set.range ↑I))
      (↑(extChartAt I x).symm ⁻¹' s ∩ Set.range ↑I) (↑(extChartAt I x) x)