∀ {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] {n : WithTop ℕ∞} {V : Type u_12}
  [inst_6 : NormedAddCommGroup V] [inst_7 : NormedSpace 𝕜 V] {f : M → 𝕜} {g : M → V},
  ContMDiff I (modelWithCornersSelf 𝕜 𝕜) n f →
    ContMDiff I (modelWithCornersSelf 𝕜 V) n g → ContMDiff I (modelWithCornersSelf 𝕜 V) n fun p => f p • g p