∀ {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'] {F : Type u_4}
  [inst_5 : NormedAddCommGroup F] [inst_6 : NormedSpace 𝕜 F] {H : Type u_5} [inst_7 : TopologicalSpace H]
  {H' : Type u_6} [inst_8 : TopologicalSpace H'] {G : Type u_7} [inst_9 : TopologicalSpace G]
  {I : ModelWithCorners 𝕜 E H} {I' : ModelWithCorners 𝕜 E' H'} {J : ModelWithCorners 𝕜 F G} {M : Type u_9}
  [inst_10 : TopologicalSpace M] [inst_11 : ChartedSpace H M] {M' : Type u_10} [inst_12 : TopologicalSpace M']
  [inst_13 : ChartedSpace H' M'] {N : Type u_11} [inst_14 : TopologicalSpace N] [inst_15 : ChartedSpace G N]
  {n m : WithTop ℕ∞} (h : Diffeomorph I J M N n) {f : N → M'} {s : Set M} {x : M},
  m ≤ n → ContMDiffWithinAt I I' m (f ∘ ⇑h) s x = ContMDiffWithinAt J I' m f (⇑h.symm ⁻¹' s) (h x)