∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {F : Type u_6} [inst_6 : NormedAddCommGroup F]
  [inst_7 : NormedSpace 𝕜 F] {F' : Type u_7} [inst_8 : NormedAddCommGroup F'] [inst_9 : NormedSpace 𝕜 F']
  {n : WithTop ℕ∞} {g : F → F'} {f : M → F},
  ContDiff 𝕜 n g → ContMDiff I (modelWithCornersSelf 𝕜 F) n f → ContMDiff I (modelWithCornersSelf 𝕜 F') n (g ∘ f)